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Organizers:
Yoram Alhassid
Boris Altshuler
Vladimir Fal'ko
Program Coordinator:
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Nuclei, Quantum Dots, and Nanostructures July 20 - August 28, 2009 Abstracts
Integrable pairing models in nuclear and mesoscopic physics
The exact solution of the SU(2) pairing Hamiltonian with non-degenerate single particle orbits was introduced by Richardson in the early sixties, although it was recovered in the last decade in an effort to describe the disappearance of superconductivity in ultrasmall grains. Since then it has been widely applied to nuclear and mesoscopic systems where finite size effects are important. Lately we have extended this family of exactly solvable models to higher rank algebras to describe pairing between multi-component fermion systems like three color cold atom gases or proton-neutron systems. In this talk I will review some of the achievements in the application of the SU(2) exact Richardson solution as well as new results for multi-component systems.
Strongly correlated phenomena associated with symmetry
breaking in small finite-size systems will be reviewed, with a focus on
the strongly correlated regime of electrons in two-dimensional
semiconductor quantum dots and trapped ultracold bosonic atoms in
harmonic traps. The talk will emphasize universal aspects and
similarities of symmetry breaking found in these systems, as well as in
more traditional fields like nuclear physics and quantum chemistry. A
complete description of the strongly correlated regime requires
approximations beyond the mean-field level. A unified description of
strongly correlated phenomena in finite systems of repelling particles
(whether fermions or bosons) has been achieved through a two-step
method of symmetry breaking at the unrestricted Hartree-Fock level and
of subsequent symmetry restoration via post Hartree-Fock projection
techniques. The general principles of the two-step method can be traced
to nuclear theory (Peierls and Yoccoz) and quantum chemistry (Lowdin).
Quantitative and qualitative aspects of the two-step method are tested
and validated by large-scale exact diagonalization calculations.
We study wave-scattering problems where the interference
pattern is so complex that only a statistical treatment is
meaningful. Complexity in wave scattering may derive from i) the
chaotic nature of the underlying classical dynamics, or ii) the quenched
randomness of the scattering potentials. Generally, we find that the
probability distributions involve certain ``relevant physical
parameters", while any other information is irrelevant: this feature has
often been captured within a maximum-entropy approach. In case i) we
consider electronic and microwave transport through chaotic cavities.
Its study employs concepts from the statistical theory of nuclear
reactions and the nuclear optical model, so that the relevant physical
parameter is the optical S matrix. We find good agreement with numerical
solutions of the Schrodinger equation. Various unexplained problems are
discussed. In case ii) we study disordered conductors and waveguides,
where the relevant physical parameter is the mean-free-path. We review
past work on the maximum-entropy approach and on a generalized
central-limit theorem that was shown later. A recent potential model
gives one further generalization of this theorem and allows the
description of certain features which were not explained by previous
work. Some unsolved problems are mentioned.
In the Coulomb blockade regime of a ballistic quantum dot, the
distribution of conductance peak spacings is well known to be
incorrectly predicted by a single-particle picture; instead, matrix
element fluctuations of the residual electronic interaction need to be
taken into account. However, a simple random-wave model for the
Hartree-Fock wave functions, valid in the semiclassical limit where the
number of electrons in the dot becomes large, predicts fluctuations that
may be too small to explain low-temperature experimental data. In a
collaboration with Y. Alhassid, we have examined matrix element
fluctuations in realistic chaotic geometries, and shown that at energies
of experimental interest these fluctuations generically exceed by a
factor of about 3-4 the predictions of the random wave model. Even
larger fluctuations occur in geometries with a mixed chaotic-regular
phase space. Among other findings, we show that the distribution of
interaction matrix elements is strongly non-Gaussian in the parameter
range of experimental interest, and that the dynamical effects behind
the enhanced fluctuations cannot be computed using a leading-order
semiclassical approach. These results may allow for much better
agreement between the Hartree-Fock picture and experiment.
In a recent work and within the context of quantized chaotic
billiards, random plane wave and semiclassical theoretical approaches
were applied to an example of a relatively new class of statistical
measures, i.e., measures involving both complete spatial integration and
energy summation as essential ingredients. A quintessential example
comes from the desire to understand the short-range approximation to the
first order ground state contribution of the residual Coulomb
interaction. Billiards, fully chaotic or otherwise, provide an ideal
class of systems on which to focus as they have proven to be successful
in modeling the single particle properties of a Landau-Fermi liquid in
typical mesoscopic systems, i.e., closed or nearly closed quantum dots.
It happens that both theoretical approaches give fully consistent
results for measure averages, but that somewhat surprisingly for fully
chaotic systems the semiclassical theory gives a much improved
approximation for the fluctuations. Comparison of the theories
highlights a couple of key shortcomings inherent in the random plane
wave approach. The case of non-fully chaotic systems is also discussed.
We study the transport and localization properties of
laser-driven quantum wires through a formalism of Floquet-Green
functions for time-periodic Hamiltonians that allows a generalization
of the definition of localization length for disordered systems and of
the Landauer formalism for the calculation of the conductance. Modifying
the laser parameters we can control in a coherent way the transport and
localization properties of quantum wires.
The measurement of any observable in quantum mechanics is a
probabilistic process described by the projection postulate. As opposed
to projective (strong) measurement, weakly measuring an observable (i.e.
measuring it while weakly disturbing the system), provides only partial
information on the state of the system. It has been proposed that a
two-step procedure --weak measurement followed by a strong one, where
the outcome of the first measurement is kept provided a second
post-selected outcome occurs-- leads to a weak value. Such a weak value
may lie well beyond the range of strong values and may happen to be
complex. We recently discuss the measurement of weak values within the
framework of solid state physics. Here we review some of the ideas
associated with weak values. We will present a proposal to observe the
weak value of electron spin in a double quantum dot with a quantum point
contact to be used as a detector. We also show how to incorporate the
adverse effect of decoherence into this procedure. The proposed protocol
is amenable of experimental realization within actual experimental
setups. We further discuss ho to implement this concept vis-a-vis the
physics of Mach-Zehnder interferometry which allows for a full
tomography of the weak values and for the generalization of weak values
to many-body systems.
Shell structure is a common phenomenon for finite-size
quantum systems. We discuss how shell structure appears in nuclei and in
ultracold atomic gases. Super-shell structure is predicted for a gas of
fermionic atoms with repulsive interaction in a 3D H.O. trap. Structural
effects in the BCS pairing gap are discussed from periodic orbit theory,
stressing the role of regularity/chaos. Results are compared to pairing
gaps obtained from nuclear masses, calculated as well as measured. Detailed structure properties of a two-component fermionic atomic
system, confined in a 2D trap, are obtained from a full numerical
diagonalization of the many-body Hamiltonian. The chemical potential
differences, excitation energies and angular momentum spectra show that
when the zero-range attractive interaction is varied in strength, strong
odd-even effects, gaps and shell structure emerge, typical for a pairing
interaction. On the other hand, for repulsive interaction we find that
the coupling scheme is characterised by Hund’s rule. Finally, we show
an example of how the numerical diagonalization of the many-body
Hamiltonian can account for larger numbers of particles, by using an
effective interaction defined in a truncated model space (Lee-Suzuki).
The surface plasmon is a collective excitation of the
conduction electrons which dominates the optical absorption spectrum in
metallic nanoparticles. The electron-hole excitations act as a thermal
bath for this quantum degree of freedom, giving rise to a width and a
frequency shift of the resonance. Using approaches of quantum
dissipative systems and semiclassical methods, we calculate these
renormalization effects for alkaline and noble-metal nanoparticles,
allowing the interpretation of pump-and-probe experiments on the
time-evolution of the transmission spectrum. Under strong laser
excitation we predict the appearance of sidebands in the absorption
spectrum. We extend our analysis to the spin-dependent dipole excitation
in alkaline nanoparticles and study its possible observation in the
photo-absorption spectrum of open-shell systems.
We investigate the competition between superconductivity and
ferromagnetism in chaotic ultrasmall metallic grains in a regime where
both phases can coexist. An effective Hamiltonian is used which combines
a BCS-like pairing term and a ferromagnetic Stoner-like spin exchange
term. We study the transport properties of the grain in the Coulomb
blockade regime and identify signatures of the coexistence between
pairing and exchange correlations in the mesoscopic fluctuations of the
conductance peak spacings and peak heights.
The LIT method, suitable for treating ab initio reactions in
the continuum of finite systems, will be described. A few results of its
applications to perturbation induced reactions with light nuclei will be
presented.
In the "Universal Hamiltonian" for quantum dots one replaces the actual electron-electron interaction by their zero mode components. Accounting for the charging and the spin exchange components of this interaction is non-trivial. While some thermodynamic observables can be treated exactly, the model leads to a non-Abelian bosonic action. So far this action has been treated in the limit of Ising spin interaction, and perturbatively in the limit of spin anisotropic exchange.
Outlining the difficulties in tackling this problem, and reviewing the progress made in the context of the anisotropic model, I will report on recent progress done with the full-fledged non-Abelian isotropic model, employing a trick due to Kolokolov. This work is in collaboration with Igor Burmistrov and Misha Kiselev.
The description of strong electronic correlations far from
thermal equilibrium is one of the outstanding open questions in the
field of mesoscopic physics. Many of the theoretical approaches that
have proven so successful in equilibrium are simply inadequate once the
system is driven out of equilibrium. In this talk I will review our
recent extension of Wilson's numerical renormalization-group approach to
track the real-time dynamics of quantum impurities following the sudden
application of a perturbation. Applications of the approach to spin and
charge relaxation in ultrasmall quantum dots, decoherence of an impurity
spin, and real-time dynamics in the spin-boson model will be discussed.
A nonequilibrium many-body theory of single-molecule junctions is developed, which treats coherent quantum effects and Coulomb interactions on an equal footing, using a realistic description of the electronic structure of the molecule. The differential conductance spectrum of a junction is shown to exhibit characteristic quantum interference effects, as well as a complex "molecular diamond" structure analogous to the regular Coulomb diamonds observed in quantum dot transport experiments. A dramatic enhancement of thermoelectric effects is predicted when the junction is tuned across a node in the transmission function.
I will discuss recent advances in Scanning SQUID Microscopy (SSM) that enable us to measure static and quasi-static magnetic moments as small as 100 electron spins in individual mesoscopic samples. We developed these techniques to measure the current in individual mesoscopic rings, one ring at a time, as a function of applied magnetic flux. I will briefly summarize results on dirty aluminum superconducting rings with a bilayer structure that leads to two weakly coupled ordered parameters, and fluctuation superconductivity in less dirty aluminum rings in the Little-Parks regime. In our recent measurements on individual gold rings we find a distribution of h/e-periodic persistent currents that is consistent with theory. Finally, I will talk about our unexpected observation of a linear susceptibility on various samples , corresponding to an area density of unpaired spins on the order of 0.4 spins/nm2. The spins on Au films appear to be weakly coupled to conduction electrons, and the out-of-phase component of the susceptibility gives direct experimental evidence for the hypothesis that the 1/f flux noise seen in SQUIDs and superconducting qubits is due to fluctuating spins.
The NLSE is relevant for the explorations of Bose-Einstein
Condensates and for Nonlinear Classical Optics. A natural question is
whether Anderson Localization survives the effect of nonlinearities in
one dimension. Relevant experimental, numerical, heuristic and rigorous
results will be presented. A perturbation expansion in the nonlinear
term was developed and used to obtain a rigorous bound on the spreading
for short times. In particular it is found that exponential localization
holds at least for time scales inversely proportional to the square of
the nonlinearity. The perturbation theory was used to obtain the values
of the wave functions for short times. Conjectures on the long time
behavior will be presented. Some results for a generalized version of
the NLSE will be presented as well. The work reported in the talk was
done in collaboration with Avy Soffer, Yevgeny Krivolapov and Hagar Veksler.
We analyze generalizations of two dimensional topological
insulators which can be realized in interacting, time reversal invariant
electron systems. These states, which we call fractional topological
insulators, contain excitations with fractional charge and statistics in
addition to protected edge modes. In the case of s^z conserving toy
models, we show that a system is a fractional topological insulator if
and only if \sigma_{sH}/e^* is odd, where \sigma_{sH} is the spin-Hall
conductance in units of e/2\pi, and e^* is the elementary charge in
units of e. We find that systems with 1/e^* even cannot support
fractional topological insulators. This work is in collaboration with
Michael Levin (Harvard).
We study the time dynamics of a single boson coupled to a
bath of two-level systems (spins 1/2) with different excitation
energies, described by an inhomogeneous Dicke model. Analyzing the
time-dependent Schrodinger equation we find that at resonance the boson
decays in time to an oscillatory state with a finite amplitude
characterized by a single Rabi frequency if the inhomogeneity is below a
certain threshold. In the limit of small inhomogeneity, the decay is
suppressed and exhibits a complex (mainly Gaussian-like) behavior,
whereas the decay is complete and of exponential form in the opposite
limit. For intermediate inhomogeneity, the boson decay is partial and
governed by a combination of exponential and power laws.
We consider low-temperature behavior of weakly interacting
electrons in disordered conductors in the regime when all
single-particle eigenstates are localized by the quenched disorder. We
prove that i the absence of coupling of the electrons to any external
bath dc electrical conductivity exactly vanishes as long as the
temperature T does not exceed some finite value T_c. At the same time,
it can be also proven that at high enough T the conductivity is finite.
These two statements imply that the system undergoes a finite
temperature Metal-to-Insulator transition, which can be viewed as
Anderson-like localization of many-body wave functions in the Fock
space. Metallic and insulating states are not different from each other
by any spatial or discrete symmetries. The recent unpublished results on
the many-body localization of weakly interacting bosons in one dimension
will be also presented.
I will discuss conductance of a quantum wire in the presence
of weak electron-electron scattering. In a sufficiently long wire the
scattering leads to full equilibration of the electron distribution
function in the frame moving with the electric current. At non-zero
temperature this equilibrium distribution differs from the one supplied
by the leads. As a result the contact resistance increases, and the
quantized conductance of the wire acquires a quadratic in temperature
correction. The magnitude of the correction is found by analysis of the
conservation laws of the system and does not depend on the details of
the interaction mechanism responsible for equilibration.
In this talk I will argue that a generic system of one-dimensional interacting fermions with a gapless excitation spectrum (the Luttinger liquid) exhibits a feature characteristic of a Fermi liquid: a Lorentzian peak in the single-particle spectral function.
We present an exact mapping of models of interacting fermions onto boson models. The bosons correspond to collective excitations in the initial fermionic models. This bosonization is applicable in any dimension and for any interaction between fermions. We show how the mapping can be used for Monte Carlo calculations and argue that it should be free from the sign problem. Introducing superfields we derive a field theory that may serve as a new way of analytical study.
We investigate the electron-mediated interaction between atoms adsorbed on the surface of monolayer graphene.
The interaction is shown to favour ordered states, whose order parameter depends on the subgroup of the lattice
symmetry group preserved by an individual impurity. The corresponding order-disorder phase transitions are studied
numerically and the corresponding critical temperatures are calculated. The signatures of the phase transitions in
transport and optical properties of the system are discussed. This work is in collaboration with O. Suljuasen,
V. Falko, and B. Altshuler.
Spectral fluctuation properties of interacting Fermion systems are often successfully modelled in terms of Dyson’s three canonical ensembles of random matrices. More realistic random-matrix models that take account of the typical two-body nature of the interaction cannot be solved analytically. It is not known whether in the limit of infinite matrix dimension the spectral fluctuations of such models agree with those of the canonical ensembles. We approach that question by considering constrained ensembles (certain matrix elements of the canonical ensembles are constrained to have the values zero). We show that up to a maximum number of constraints the spectral fluctuations of these constrained ensembles coincide with those of the canonical ensembles.
One speaks of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. We approach the question by using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. We show that chaos is a generic feature of the ensemble and display some of its properties, emphasizing those which differ from standard random-matrix theory. In particular, we display the existence of correlations among spectra carrying different quantum numbers. These are subject to experimental verification.
We study the non-equilibrium dynamics following a quantum quench of a single-spin in a semiconductor quantum dot adjacent to a Fermionic reservoir and show how the dynamics can be revealed in detail in an optical absorption experiment. We show that the highly asymmetrical optical absorption lineshape of the resulting Kondo exciton consists of three distinct frequency domains, corresponding to short, intermediate and long times after the initial excitation, which are in turn described by the three fixed points of the single-impurity Anderson Hamiltonian. In particular, the zero temperature power-law singularity dominating the lineshape is linked to dynamically generated Kondo correlations in the photo-excited state.
Single atom carbon chains (SACC) are natural candidates for molecular scale interconnects in carbon based electronic devices. Recently such interconnects have been observed in mechanically stretched graphene nanoribbons. Previous theoretical studies of electron transport through SACC were numerical and assumed metallic leads. I will report on a recent analytical study of conductance of an SACC interconnect between two graphene leads. Electron transport through the device is qualitatively different from that in the case of normal metal leads. It proceeds via narrow resonant states in the wire, arising from the small density of states in the leads at low energy. The energy dependence of the transmission coefficient near resonance is asymmetric and acquires a universal form at small energies. In the case of leads
with the zigzag edges the dispersion of the edge states has a significant effect on the device conductance.
Graphene is the first real two-dimensional solid consisting of a hexagonal lattice of carbon atoms, revealing a high carrier mobility and quantum Hall effect at room temperature. First graphene quantu devices have been recently demonstrated, such as graphene nanoribbons, quantum interference devices, and graphene single electron transistors. Here, we report measurements on graphene quantum dots. We show that excited single-particle states can be detected in graphene quantum dots via cotunneling in the Coulomb blockaded regime as well as via related features for high voltage bias. The devices consisting of single-layer graphene islands with diameters in the range of 50 to 140 nm are connected via two narrow graphene constrictions and are tunable by a lateral graphene gates. From transport measurements we extract charging energies in the order 0f around 10 meV and single-level spacings on the order of a few meV. Furthermore we demonstrate the functionality of a charge-read-out using a nearby graphene constriction. Both steps, the detection of excited states and the charge-read-out are crucial for the investigation of graphene quantum devices in general as well as for future implementations of spin qubits in graphene. In particular it allows to relate the size of the quantum dot to the relevant energy scales such as charging energy and quantum confinement energy. Finally, we discuss the magnetic field dependence of the electronic levels in both the hole and electron regime.
Upon increasing the density of electrons in a quantum wire, the system undergoes a transition from a one-dimensional to a quasi-one-dimensional state. We study the properties of this quantum phase transition as a function of the interaction strength. In the absence of interactions between electrons, it corresponds to filling up the second subband of transverse quantization. On the other hand, strongly interacting one-dimensional electrons form a Wigner crystal, and the transition corresponds to it splitting into two chains (zigzag crystal). In this regime, the effective Hamiltonian is represented by two weakly coupled modes given by a Luttinger liquid and a transverse field Ising model. Performing a renormalization group analysis, we show that the critical fixed point is Lorentz invariant. However, the critical velocity vanishes due to marginally irrelevant operators. This entails, e.g., a diverging specific heat coefficient.
In this talk I will give a short review of the knowledge
about many-body quantum chaos accumulated in our work and show with few examples how this knowledge can be used as a theoretical, experimental and computational tool. Special topics for discussion will be relation between chaos and thermalization, chaotic enhancement of weak perturbations and exponential convergence of large Hamiltonian matrices.
We study the interplay of intrinsic chaos and irreversible decay into open continuum channels in an open Fermi-system model. The results are applicable both to various mesoscopic objects, including the conductance fluctuations, and to resonance nuclear reactions. Two models are considered: with one-body chaos that is due to disorder, and many-body chaos resulting from interaction between particles. The coupling to continuum is described by effective non-Hermitian Hamiltonian. The correlations of cross-sections manifest specific dependence on the degree of intrinsic chaos.
We first review the system of unitarity fermions, which we interpret as a UV fixed point of a quantum field theory. We then discuss the Schroedinger group, which is the group of symmetry of unitarity fermions, and is a nonrelativistic version of conformal symmetry. We then construct a spacetime whose symmetry is the Schroedinger symmetry. We speculate on a possible holographic dual of unitarity fermions, and discuss recent string-theoretic approaches to the problem.
With attosecond light pulses and the X-ray Free Electron Lasers in Hamburg and Stanford being built a new regime of light-matter coupling can be realized, where energy of high spatial density can be transferred from the light to matter in a short time (on the order of 10 femtoseconds). Clusters of finite size (from some 10 to millions of atoms) are an ideal target for these light pulses since they provide the high particle density from solids combined with the possibility to form a beam (like an atomic beam) to be crossed with the light beam. Examples of fast non-equilibrium processes along with their experimental realization will be discussed.
One-dimensional quantum fluids are conventionally described by
using an effective hydrodynamic approach known as Luttinger liquid
theory. As its principal simplification, a generic spectrum of the
constituent particles is replaced by a linear one. To evaluate the
momentum-resolved dynamic responses, however, one needs to account for
the nonlinearity of the particles spectrum. The hallmark of the new
nonlinear theory are the universal singularities in the dynamic response
functions.
We will discuss quantum dots containing up to two resonant
levels coupled to different geometries of leads and charge sensors
(quantum point contacts). The dot is also coupled electrostatically to a
side-gate used to tune its population. We shall show that for certain
geometries the charge of the dot exhibits an abrupt change as function
of the applied gate voltage, corresponding to a first order phase
transition. The existence of the phase transition depends on the
competition between the Anderson orthogonality catastrophe and the Mahan
exciton in each geometry.
The major contribution to decoherence of quantum dot or
Josephson junction charge qubits comes from the electrostatic coupling
to impurities whose charge fluctuates due to hybridization with
electrons in the reservoir. However, estimating the efficiency of such
``fluctuators'' for decoherence according to the previously developed
theories shows that finding a sufficient number of effective fluctuators
in a realistic experimental layout is rather improbable. We show that
this paradox is resolved by allowing for a short-range Coulomb
interaction of the fluctuators with the electrons in the reservoir
dramatically enhances both their contribution to decoherence and the
estimate of the number of effective fluctuators, resulting in the most
dangerous decoherence mechanism for charge qubits.
We study the RPA equations in their general form by taking the
matrix elements appearing in the RPA equations as random variables. The
spectrum of the resulting random-matrix model is determined by solving a
generalized Pastur equation. Two independent dimensionless parameters
govern the behaviour of the system: the distance between the centers of
positive and negative eigenvalues and the strength of their coupling. By
increasing this coupling the two original semicircles are deformed and
pulled toward each other, till they begin to overlap and as a
consequence, the system becomes unstable and eigenvalues leave the real
axis. This work is in collaboration with X.Barillier-Pertruisel and
H.Weidenmueller.
Parity violation in the compound nucleus is reviewed.
Generically, enhancement factors amplify the signal for symmetry
breaking, and the stochastic properties allow the strength of the
symmetry-breaking interaction to be inferred from that signal without
the need to know the wavefunctions of individual states. The scattering
of spin-polarized neutrons by medium and heavy nuclei provides signals
for parity violation at the percent level. The statistical analysis of
the data yields values for the spreading width about 10$^{-6}$ eV in
keeping with theoretical expectations.
The existence of an equilibrium persistent current (PC) in a non-superconducting mesoscopic system having a finite resistance is one of the surprising fundamental results that characterize the Physics on these scales. We consider the magnitude of these currents in a very low-temperature superconductor with a bare transition temperature much smaller than the Thouless energy. To resolve the long-standing discrepancy between the theoretical and experimental values (especially for Copper) for the magnitude of the average currents for the noble metals, we capitalize on the recent finding that these metals almost always have some magnetic impurities which dominate their dephasing rates at low T. We show that in a rather broad range of pair-breaking rates, much larger than the bare transition temperature, but much smaller than the Thouless scale, the transition temperature is renormalized to zero, but the PC is hardly affected. This increases the predicted magnitudes of the PC and may provide an explanation for the values (and signs) of the average PC's in Gold and in Copper, as well as a way to determine their "bare" transition temperatures (those that would exist without the pair-breaking magnetic impurities).
This work is in collaboration with Hamutal Bary-Soroker and Ora Entin-Wohlman. It can be found in Cond-Mat 0804.0702 and Phys. Rev. Lett., 101, 057001 (2008). It is reviewed by H. Bouchiat in http://physics.aps.org/articles/v1/7.
The trajectory-based semiclassical approach is often blamed for having little predictive power. Specifying to ballistic systems,
it faithfully reproduces random matrix theory results for the conductance and its fluctuations, shot noise aso. In presence of spin orbit interaction, it allows to obtain weak antilocalization and appropriately describes spin relaxation - but again does not deliver any fundamentally new result. In this talk I will use both semiclassics and random matrix theory to calculate the spin conductance and its fluctuations in ballistic mesoscopic systems with spin-orbit interactions. I will show that semiclassics predicts a finite average spin conductance, whereas this quantity vanishes in random matrix theory.
We measure tunneling through a single quantum level in a carbon nanotube quantum dot connected to resistive metal leads. For the electrons tunneling to/from the nanotube, the leads serve as a dissipative environment, which suppresses the tunneling rate. In the regime of sequential tunneling, the height of the single-electron conductance peaks increases as the temperature is lowered, although it scales more weakly than the conventional ~1/T. In the resonant tunneling regime (temperature smaller than the level width), the peak width approaches saturation, while the peak height starts to _decrease_. Overall, the peak height shows a non-monotonic temperature dependence. We associate this unusual behavior with the transition from the sequential to the resonant tunneling through a single quantum level in a dissipative environment. We draw a connection between our results and the recent theories on a quantum dot with Luttinger liquid leads.
We studied the influence of a slow classical noise on Landau-Zener transitions. We demonstrated that slow colored noise characterized by correlation time much greater compared to Landau-Zener time can produce transition itself or can change substantially the Landau-Zener transition probabilities. Exact formulas for finite time probabilities are derived by solving equation of motion for the density matrix. Connections between the slow noise induced Landau-Zener theory and recent experiments on double quantum dots are discussed.
I will summarize our results and ambitions in studying two examples of phase transitions in nanoscale samples. In the first we take nanoscale crytals of materials which exhibit phase transitions in the bulk, such as vanadium dioxide with its first order metal-insulator transition at 67 C. In the second, we investigate phase transitions in a cylindrical monolayer of atoms adsorbed on a suspended carbon nanotube.
The simple relation between magnetic and rotational response is discussed for the cyclotron radius being much larger than the size of the system. Nuclei, metallic clusters, and quantum dots in the ballistic regime are considered. The response in the unpaired state is determined by the quantal properties of the orbitals in the mean potential. The properties of the smallest systems (N<50) derive from the geometry of the individual orbits, whereas the gross features of medium-size systems (N~100 -1000) are interpreted in term of classical periodic orbits. For paired state, the response of systems with a size smaller than the coherence length is discussed.
We consider the Cooper instability at a very strong disorder where single-particle states are nearly critical or localized. Fermions are supposed to interact via point-like attractive interaction, with
long-range Coulomb interaction absent. We show that the near-critical disorder enhances superconductive transition temperature. Application to cold fermion atoms in disordered optical lattices is discussed.
During the talk I would like to discuss the properties of dilute and strongly interacting Fermi gas in the unitary regime. I will report on results for the energy, entropy and chemical potential as a function of temperature and give upper bounds on the critical temperature for the onset of superfluidity. The comparison with recent measurements of the entropy and of the critical temperature of a trapped unitary Fermi gas will be presented. I will present also the first ab initio evaluation of the one-body temperature propagator of the unitary Fermi gas, free of uncontrolled approximations, which allows for the extraction of the temperature dependence of the pairing (pseudo)gap. I will show that the spectral weight function for the system can be accurately parametrized by three functions of temperature: an effective mass, a mean-field potential, and a gap. Surprisingly, below the critical temperature these quantities can be accurately reproduced using an independent quasiparticle model. If time allows I will also discuss superfluid properties of a similar system - dilute neutron matter. |