17 research outputs found
<em>P</em>-wave superfluidity of atomic lattice fermions
We discuss the emergence of p-wave superfluidity of identical atomic fermions
in a two-dimensional optical lattice. The optical lattice potential manifests
itself in an interplay between an increase in the density of states on the
Fermi surface and the modification of the fermion-fermion interaction
(scattering) amplitude. The density of states is enhanced due to an increase of
the effective mass of atoms. In deep lattices the scattering amplitude is
strongly reduced compared to free space due to a small overlap of wavefunctions
of fermion sitting in the neighboring lattice sites, which suppresses the
p-wave superfluidity. However, for moderate lattice depths the enhancement of
the density of states can compensate the decrease of the scattering amplitude.
Moreover, the lattice setup significantly reduces inelastic collisional losses,
which allows one to get closer to a p-wave Feshbach resonance. This opens
possibilities to obtain the topological superfluid phase, especially
in the recently proposed subwavelength lattices. We demonstrate this for the
two-dimensional version of the Kronig-Penney model allowing a transparent
physical analysis.Comment: 12 pages, 4 figures; published versio
Commensurability effects in one-dimensional Anderson localization: anomalies in eigenfunction statistics
The one-dimensional (1d) Anderson model (AM) has statistical anomalies at any
rational point , where is the lattice constant and
is the de Broglie wavelength. We develop a regular approach to
anomalous statistics of normalized eigenfunctions at such
commensurability points. The approach is based on an exact integral
transfer-matrix equation for a generating function ( and
have a meaning of the squared amplitude and phase of eigenfunctions,
is the position of the observation point). The descender of the generating
function is shown to be the
distribution function of phase which determines the Lyapunov exponent and the
local density of states.
In the leading order in the small disorder we have derived a second-order
partial differential equation for the -independent ("zero-mode") component
at the () anomaly. This equation is
nonseparable in variables and . Yet, we show that due to a hidden
symmetry, it is integrable and we construct an exact solution for explicitly in quadratures. Using this solution we have computed moments
() for a chain of the length and found an essential difference between their -behavior in the
center-of-band anomaly and for energies outside this anomaly. Outside the
anomaly the "extrinsic" localization length defined from the Lyapunov exponent
coincides with that defined from the inverse participation ratio ("intrinsic"
localization length). This is not the case at the anomaly where the
extrinsic localization length is smaller than the intrinsic one.Comment: 33 pages, four figure
Conductance Fluctuations of Open Quantum Dots under Microwave Radiation
We develop a time dependent random matrix theory describing the influence of
a time-dependent perturbation on mesoscopic conductance fluctuations in open
quantum dots. The effect of external field is taken into account to all orders
of perturbation theory, and our results are applicable to both weak and strong
fields. We obtain temperature and magnetic field dependences of conductance
fluctuations. The amplitude of conductance fluctuations is determined by
electron temperature in the leads rather than by the width of electron
distribution function in the dot. The asymmetry of conductance with respect to
inversion of applied magnetic field is the main feature allowing to distinguish
the effect of direct suppression of quantum interference from the simple
heating if the frequency of external radiation is larger than the temperature
of the leads .Comment: 7 pages, 5 figure
Quantum correction to the Kubo formula in closed mesoscopic systems
We study the energy dissipation rate in a mesoscopic system described by the
parametrically-driven random-matrix Hamiltonian H[\phi(t)] for the case of
linear bias \phi=vt. Evolution of the field \phi(t) causes interlevel
transitions leading to energy pumping, and also smears the discrete spectrum of
the Hamiltonian. For sufficiently fast perturbation this smearing exceeds the
mean level spacing and the dissipation rate is given by the Kubo formula. We
calculate the quantum correction to the Kubo result that reveals the original
discreteness of the energy spectrum. The first correction to the system
viscosity scales proportional to v^{-2/3} in the orthogonal case and vanishes
in the unitary case.Comment: 4 pages, 3 eps figures, REVTeX
Charged hydrogenic problem in a magnetic field: Non-commutative translations, unitary transformations, and coherent states
An operator formalism is developed for a description of charged electron-hole
complexes in magnetic fields. A novel unitary transformation of the Hamiltonian
that allows one to partially separate the center-of-mass and internal motions
is proposed. We study the operator algebra that leads to the appearance of new
effective particles, electrons and holes with modified interparticle
interactions, and their coherent states in magnetic fields. The developed
formalism is used for studying a two-dimensional negatively charged
magnetoexciton . It is shown that Fano-resonances are present in the
spectra of internal transitions, indicating the existence of
three-particle quasi-bound states embedded in the continuum of higher Landau
levels.Comment: 9 pages + 2 figures, accepted in PRB, a couple of typos correcte
Which Kubo formula gives the exact conductance of a mesoscopic disordered system?
In both research and textbook literature one often finds two ``different''
Kubo formulas for the zero-temperature conductance of a non-interacting Fermi
system. They contain a trace of the product of velocity operators and
single-particle (retarded and advanced) Green operators: or . The study investigates the relationship between
these expressions, as well as the requirements of current conservation, through
exact evaluation of such quantum-mechanical traces for a nanoscale (containing
1000 atoms) mesoscopic disordered conductor. The traces are computed in the
semiclassical regime (where disorder is weak) and, more importantly, in the
nonperturbative transport regime (including the region around
localization-delocalization transition) where concept of mean free path ceases
to exist. Since quantum interference effects for such strong disorder are not
amenable to diagrammatic or nonlinear -model techniques, the evolution
of different Green function terms with disorder strength provides novel insight
into the development of an Anderson localized phase.Comment: 7 pages, 5 embedded EPS figures, final published version (note: PRB
article has different title due to editorial censorship
Dimers, Effective Interactions, and Pauli Blocking Effects in a Bilayer of Cold Fermionic Polar Molecules
We consider a bilayer setup with two parallel planes of cold fermionic polar
molecules when the dipole moments are oriented perpendicular to the planes. The
binding energy of two-body states with one polar molecule in each layer is
determined and compared to various analytic approximation schemes in both
coordinate- and momentum-space. The effective interaction of two bound dimers
is obtained by integrating out the internal dimer bound state wave function and
its robustness under analytical approximations is studied. Furthermore, we
consider the effect of the background of other fermions on the dimer state
through Pauli blocking, and discuss implications for the zero-temperature
many-body phase diagram of this experimentally realizable system.Comment: 18 pages, 10 figures, accepted versio
Temporal fluctuations of waves in weakly nonlinear disordered media
We consider the multiple scattering of a scalar wave in a disordered medium
with a weak nonlinearity of Kerr type. The perturbation theory, developed to
calculate the temporal autocorrelation function of scattered wave, fails at
short correlation times. A self-consistent calculation shows that for
nonlinearities exceeding a certain threshold value, the multiple-scattering
speckle pattern becomes unstable and exhibits spontaneous fluctuations even in
the absence of scatterer motion. The instability is due to a distributed
feedback in the system "coherent wave + nonlinear disordered medium". The
feedback is provided by the multiple scattering. The development of instability
is independent of the sign of nonlinearity.Comment: RevTeX, 15 pages (including 5 figures), accepted for publication in
Phys. Rev.
Non-adiabatic charge pump: an exact solution
We derived a general and exact expression of current for quantum parametric
charge pumps in the non-adiabatic regime at finite pumping frequency and finite
driving amplitude. The non-perturbative theory predicts a remarkable plateau
structure in the pumped current due to multi-photon assisted processes in a
double-barrier quantum well pump involving only a {\it single} pumping
potential. It also predicts a current reversal as the resonant level of the
pump crosses the Fermi energy of the leads
Effects of quantum interference in spectra of cascade spontaneous emission from multilevel systems
A general expression for the spectrum of cascade spontaneous emission from an arbitrary multilevel system is presented. Effects of the quantum interference of photons emitted in different transitions are analyzed. These effects are especially essential when the transition frequencies are close. Several examples are considered: (i) Three-level system; (ii) Harmonic oscillator; (iii) System with equidistant levels and equal rates of the spontaneous decay for all the transitions; (iv) Dicke superradiance model