37 research outputs found
Correlation-induced localization
A new paradigm of Anderson localization caused by correlations in the
long-range hopping along with uncorrelated on-site disorder is considered which
requires a more precise formulation of the basic localization-delocalization
principles. A new class of random Hamiltonians with translation-invariant
hopping integrals is suggested and the localization properties of such models
are established both in the coordinate and in the momentum spaces alongside
with the corresponding level statistics. Duality of translation-invariant
models in the momentum and coordinate space is uncovered and exploited to find
a full localization-delocalization phase diagram for such models. The crucial
role of the spectral properties of hopping matrix is established and a new
matrix inversion trick is suggested to generate a one-parameter family of
equivalent localization/delocalization problems. Optimization over the free
parameter in such a transformation together with the
localization/delocalization principles allows to establish exact bounds for the
localized and ergodic states in long-range hopping models. When applied to the
random matrix models with deterministic power-law hopping this transformation
allows to confirm localization of states at all values of the exponent in
power-law hopping and to prove analytically the symmetry of the exponent in the
power-law localized wave functions.Comment: 14 pages, 8 figures + 5 pages, 2 figures in appendice
Time-reversal symmetric Crooks and Gallavotti-Cohen fluctuation relations in driven classical Markovian systems
In this paper, we address an important question of the relationship between
fluctuation theorems for the dissipated work with general
finite-time (like Jarzynski equality and Crooks relation) and infinite-time
(like Gallavotti-Cohen theorem) drive protocols and their time-reversal
symmetric versions. The relations between these kinds of fluctuation relations
are uncovered based on the examples of a classical Markovian -level system.
Further consequences of these relations are discussed with respect to the
possible experimental verifications.Comment: 21 pages, 4 figures, 1 table, 70 references, 4 appendice
Quasiparticle trapping in Meissner and vortex states of mesoscopic superconductors
Nowadays superconductors serve in numerous applications, from high-field
magnets to ultra-sensitive detectors of radiation. Mesoscopic superconducting
devices, i.e. those with nanoscale dimensions, are in a special position as
they are easily driven out of equilibrium under typical operating conditions.
The out-of-equilibrium superconductors are characterized by non-equilibrium
quasiparticles. These extra excitations can compromise the performance of
mesoscopic devices by introducing, e.g., leakage currents or decreased
coherence times in quantum devices. By applying an external magnetic field, one
can conveniently suppress or redistribute the population of excess
quasiparticles. In this article we present an experimental demonstration and a
theoretical analysis of such effective control of quasiparticles, resulting in
electron cooling both in the Meissner and vortex states of a mesoscopic
superconductor. We introduce a theoretical model of quasiparticle dynamics
which is in quantitative agreement with the experimental data
Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
We study analytically and numerically the dynamics of the generalized
Rosenzweig-Porter model, which is known to possess three distinct phases:
ergodic, multifractal and localized phases. Our focus is on the survival
probability , the probability of finding the initial state after time
. In particular, if the system is initially prepared in a highly-excited
non-stationary state (wave packet) confined in space and containing a fixed
fraction of all eigenstates, we show that can be used as a dynamical
indicator to distinguish these three phases. Three main aspects are identified
in different phases. The ergodic phase is characterized by the standard
power-law decay of with periodic oscillations in time, surviving in the
thermodynamic limit, with frequency equals to the energy bandwidth of the wave
packet. In multifractal extended phase the survival probability shows an
exponential decay but the decay rate vanishes in the thermodynamic limit in a
non-trivial manner determined by the fractal dimension of wave functions.
Localized phase is characterized by the saturation value of ,
finite in the thermodynamic limit , which approaches
in this limit.Comment: 21 pages, 12 figures, 61 reference
On-chip Maxwell's demon as an information-powered refrigerator
We present an experimental realization of an autonomous Maxwell's Demon,
which extracts microscopic information from a System and reduces its entropy by
applying feedback. It is based on two capacitively coupled single electron
devices, both integrated on the same electronic circuit. This setup allows a
detailed analysis of the thermodynamics of both the Demon and the System as
well as their mutual information exchange. The operation of the Demon is
directly observed as a temperature drop in the System. We also observe a
simultaneous temperature rise in the Demon arising from the thermodynamic cost
of generating the mutual information.Comment: 10 pages, 7 figure
Andreev transport in two-dimensional normal-superconducting systems in strong magnetic fields
The conductance in two-dimensional (2D) normal-superconducting (NS) systems
is analyzed in the limit of strong magnetic fields when the transport is
mediated by the electron-hole states bound to the sample edges and NS
interface, i.e., in the Integer Quantum Hall Effect regime.The Andreev-type
process of the conversion of the quasiparticle current into the superflow is
shown to be strongly affected by the mixing of the edge states localized at the
NS and insulating boundaries. The magnetoconductance in 2D NS structures is
calculated for both quadratic and Dirac-like normal state spectra. Assuming a
random scattering of the edge modes we analyze both the average value and
fluctuations of conductance for an arbitrary number of conducting channels.Comment: 5 pages, 1 figur
Electron-phonon heat transfer in giant vortex states
We examine energy relaxation of nonequilibrium quasiparticles (QPs) in different vortex configurations in "dirty" s-wave superconductors (SCs). The heat flow from the electronic subsystem to phonons in a mesoscopic SC disk with a radius of the order of several coherence lengths is calculated both in the Meissner and in the giant vortex states using the Usadel approach. The recombination process is shown to be strongly affected by interplay of the subgap states, located in the vortex core and in the region at the sample edge where the spectral gap Eg is reduced by the Meissner currents. In order to uncover the physical origin of the results, we develop a semiquantitative analytical approximation based on the combination of homogeneous solutions of Usadel equations in Meissner and vortex states of a mesoscopic SC disk and analytically calculate the corresponding spatially resolved electron-phonon heat rates. Our approach provides important information about nonequilibrium QPs cooling by the magnetic field-induced traps in various mesoscopic SC devices
Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
In this paper we suggest an extension of the Rosenzweig-Porter (RP) model,
the LN-RP model, in which the off-diagonal matrix elements have a wide,
log-normal distribution. We argue that this model is more suitable to describe
a generic many body localization problem. In contrast to RP model, in LN-RP
model a fragile weakly ergodic phase appears that is characterized by broken
basis-rotation symmetry which the fully-ergodic phase, also present in this
model, strictly respects in the thermodynamic limit. Therefore, in addition to
the localization and ergodic transitions in LN-RP model there exists also the
transition between the two ergodic phases (FWE transition). We suggest new
criteria of stability of the non-ergodic phases which give the points of
localization and ergodic transitions and prove that the Anderson localization
transition in LN-RP model involves a jump in the fractal dimension of the
eigenfunction support set. We also formulate the criterion of FWE transition
and obtain the full phase diagram of the model. We show that truncation of the
log-normal tail shrinks the region of weakly-ergodic phase and restores the
multifractal and the fully-ergodic phases.Comment: 12 pages, 7 figures, 1 table, 76 references + 7 pages, 7 figures, 1
table in Appendices. Added the justification of fractal structure of
minibands (Sec. IX, Fig. 7