133 research outputs found
Quantum pumping and dissipation: from closed to open systems
Current can be pumped through a closed system by changing parameters (or
fields) in time. The Kubo formula allows to distinguish between dissipative and
non-dissipative contributions to the current. We obtain a Green function
expression and an matrix formula for the associated terms in the
generalized conductance matrix: the "geometric magnetism" term that corresponds
to adiabatic transport; and the "Fermi golden rule" term which is responsible
to the irreversible absorption of energy. We explain the subtle limit of an
infinite system, and demonstrate the consistency with the formulas by Landauer
and Buttiker, Pretre and Thomas. We also discuss the generalization of the
fluctuation-dissipation relation, and the implications of the Onsager
reciprocity.Comment: 4 page paper, 1 figure (published version) + 2 page appendi
Classical and quantum pumping in closed systems
Pumping of charge (Q) in a closed ring geometry is not quantized even in the
strict adiabatic limit. The deviation form exact quantization can be related to
the Thouless conductance. We use Kubo formalism as a starting point for the
calculation of both the dissipative and the adiabatic contributions to Q. As an
application we bring examples for classical dissipative pumping, classical
adiabatic pumping, and in particular we make an explicit calculation for
quantum pumping in case of the simplest pumping device, which is a 3 site
lattice model.Comment: 5 pages, 3 figures. The long published version is cond-mat/0307619.
This is the short unpublished versio
Adiabatic response for Lindblad dynamics
We study the adiabatic response of open systems governed by Lindblad
evolutions. In such systems, there is an ambiguity in the assignment of
observables to fluxes (rates) such as velocities and currents. For the
appropriate notion of flux, the formulas for the transport coefficients are
simple and explicit and are governed by the parallel transport on the manifold
of instantaneous stationary states. Among our results we show that the response
coefficients of open systems, whose stationary states are projections, is given
by the adiabatic curvature.Comment: 33 pages, 4 figures, accepted versio
Scattering Theory of Dynamic Electrical Transport
We have developed a scattering matrix approach to coherent transport through
an adiabatically driven conductor based on photon-assisted processes. To
describe the energy exchange with the pumping fields we expand the Floquet
scattering matrix up to linear order in driving frequency.Comment: Proceedings QMath9, September 12th-16th, 2004, Giens, Franc
Adiabatic theorems for generators of contracting evolutions
We develop an adiabatic theory for generators of contracting evolution on
Banach spaces. This provides a uniform framework for a host of adiabatic
theorems ranging from unitary quantum evolutions through quantum evolutions of
open systems generated by Lindbladians all the way to classically driven
stochastic systems. In all these cases the adiabatic evolution approximates, to
lowest order, the natural notion of parallel transport in the manifold of
instantaneous stationary states. The dynamics in the manifold of instantaneous
stationary states and transversal to it have distinct characteristics: The
former is irreversible and the latter is transient in a sense that we explain.
Both the gapped and gapless cases are considered. Some applications are
discussed.Comment: 31 pages, 4 figures, replaced by the version accepted for publication
in CM
Charge Deficiency, Charge Transport and Comparison of Dimensions
We study the relative index of two orthogonal infinite dimensional
projections which, in the finite dimensional case, is the difference in their
dimensions. We relate the relative index to the Fredholm index of appropriate
operators, discuss its basic properties, and obtain various formulas for it. We
apply the relative index to counting the change in the number of electrons
below the Fermi energy of certain quantum systems and interpret it as the
charge deficiency. We study the relation of the charge deficiency with the
notion of adiabatic charge transport that arises from the consideration of the
adiabatic curvature. It is shown that, under a certain covariance,
(homogeneity), condition the two are related. The relative index is related to
Bellissard's theory of the Integer Hall effect. For Landau Hamiltonians the
relative index is computed explicitly for all Landau levels.Comment: 23 pages, no figure
Quantum pumping: Coherent Rings versus Open Conductors
We examine adiabatic quantum pumping generated by an oscillating scatterer
embedded in a one-dimensional ballistic ring and compare it with pumping caused
by the same scatterer connected to external reservoirs. The pumped current for
an open conductor, paradoxically, is non-zero even in the limit of vanishing
transmission. In contrast, for the ring geometry the pumped current vanishes in
the limit of vanishing transmission. We explain this paradoxical result and
demonstrate that the physics underlying adiabatic pumping is the same in open
and in closed systems.Comment: 4 pages, 2 figure
General Adiabatic Evolution with a Gap Condition
We consider the adiabatic regime of two parameters evolution semigroups
generated by linear operators that are analytic in time and satisfy the
following gap condition for all times: the spectrum of the generator consists
in finitely many isolated eigenvalues of finite algebraic multiplicity, away
from the rest of the spectrum. The restriction of the generator to the spectral
subspace corresponding to the distinguished eigenvalues is not assumed to be
diagonalizable. The presence of eigenilpotents in the spectral decomposition of
the generator forbids the evolution to follow the instantaneous eigenprojectors
of the generator in the adiabatic limit. Making use of superadiabatic
renormalization, we construct a different set of time-dependent projectors,
close to the instantaneous eigeprojectors of the generator in the adiabatic
limit, and an approximation of the evolution semigroup which intertwines
exactly between the values of these projectors at the initial and final times.
Hence, the evolution semigroup follows the constructed set of projectors in the
adiabatic regime, modulo error terms we control
On the Lipschitz continuity of spectral bands of Harper-like and magnetic Schroedinger operators
We show for a large class of discrete Harper-like and continuous magnetic
Schrodinger operators that their band edges are Lipschitz continuous with
respect to the intensity of the external constant magnetic field. We generalize
a result obtained by J. Bellissard in 1994, and give examples in favor of a
recent conjecture of G. Nenciu.Comment: 15 pages, accepted for publication in Annales Henri Poincar
Effective dynamics for particles coupled to a quantized scalar field
We consider a system of N non-relativistic spinless quantum particles
(``electrons'') interacting with a quantized scalar Bose field (whose
excitations we call ``photons''). We examine the case when the velocity v of
the electrons is small with respect to the one of the photons, denoted by c
(v/c= epsilon << 1). We show that dressed particle states exist (particles
surrounded by ``virtual photons''), which, up to terms of order (v/c)^3, follow
Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic
energies of the particles and Coulomb-like pair potentials at order (v/c)^0 and
the velocity dependent Darwin interaction and a mass renormalization at order
(v/c)^{2}. Beyond that order the effective dynamics are expected to be
dissipative.
The main mathematical tool we use is adiabatic perturbation theory. However,
in the present case there is no eigenvalue which is separated by a gap from the
rest of the spectrum, but its role is taken by the bottom of the absolutely
continuous spectrum, which is not an eigenvalue.
Nevertheless we construct approximate dressed electrons subspaces, which are
adiabatically invariant for the dynamics up to order (v/c)\sqrt{\ln
(v/c)^{-1}}. We also give an explicit expression for the non adiabatic
transitions corresponding to emission of free photons. For the radiated energy
we obtain the quantum analogue of the Larmor formula of classical
electrodynamics.Comment: 67 pages, 2 figures, version accepted for publication in
Communications in Mathematical Physic
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