51 research outputs found
Nonequilibrium transport through quantum-wire junctions and boundary defects for free massless bosonic fields
We consider a model of quantum-wire junctions where the latter are described
by conformal-invariant boundary conditions of the simplest type in the
multicomponent compactified massless scalar free field theory representing the
bosonized Luttinger liquids in the bulk of wires. The boundary conditions
result in the scattering of charges across the junction with nontrivial
reflection and transmission amplitudes. The equilibrium state of such a system,
corresponding to inverse temperature and electric potential , is
explicitly constructed both for finite and for semi-infinite wires. In the
latter case, a stationary nonequilibrium state describing the wires kept at
different temperatures and potentials may be also constructed. The main result
of the present paper is the calculation of the full counting statistics (FCS)
of the charge and energy transfers through the junction in a nonequilibrium
situation. Explicit expressions are worked out for the generating function of
FCS and its large-deviations asymptotics. For the purely transmitting case they
coincide with those obtained in the litterature, but numerous cases of
junctions with transmission and reflection are also covered. The large
deviations rate function of FCS for charge and energy transfers is shown to
satisfy the fluctuation relations and the expressions for FCS obtained here are
compared with the Levitov-Lesovic formulae.Comment: 50 pages, 24 figure
Bulk-Edge correspondence for two-dimensional Floquet topological insulators
Floquet topological insulators describe independent electrons on a lattice
driven out of equilibrium by a time-periodic Hamiltonian, beyond the usual
adiabatic approximation. In dimension two such systems are characterized by
integer-valued topological indices associated to the unitary propagator,
alternatively in the bulk or at the edge of a sample. In this paper we give new
definitions of the two indices, relying neither on translation invariance nor
on averaging, and show that they are equal. In particular weak disorder and
defects are intrinsically taken into account. Finally indices can be defined
when two driven sample are placed next to one another either in space or in
time, and then shown to be equal. The edge index is interpreted as a quantized
pumping occurring at the interface with an effective vacuum.Comment: 28 pages, 5 figures Minor changes, update and addition of some
references To appear in Annales Henri Poincar\'
Spin Conductance and Spin Conductivity in Topological Insulators: Analysis of Kubo-like terms
We investigate spin transport in 2-dimensional insulators, with the long-term
goal of establishing whether any of the transport coefficients corresponds to
the Fu-Kane-Mele index which characterizes 2d time-reversal-symmetric
topological insulators. Inspired by the Kubo theory of charge transport, and by
using a proper definition of the spin current operator, we define the Kubo-like
spin conductance and spin conductivity . We prove
that for any gapped, periodic, near-sighted discrete Hamiltonian, the above
quantities are mathematically well-defined and the equality holds true. Moreover, we argue that the physically relevant
condition to obtain the equality above is the vanishing of the mesoscopic
average of the spin-torque response, which holds true under our hypotheses on
the Hamiltonian operator. This vanishing condition might be relevant in view of
further extensions of the result, e.g. to ergodic random discrete Hamiltonians
or to Schr\"odinger operators on the continuum. A central role in the proof is
played by the trace per unit volume and by two generalizations of the trace,
the principal value trace and it directional version.Comment: 35 pages, 2 figure
A note on adiabatic time evolution and quasi-static processes in translation-invariant quantum systems
We study the slowly varying, non-autonomous quantum dynamics of a translation
invariant spin or fermion system on the lattice . This system is
assumed to be initially in thermal equilibrium, and we consider realizations of
quasi-static processes in the adiabatic limit. By combining the Gibbs
variational principle with the notion of quantum weak Gibbs states introduced
in [Jak\v{s}i\'c, Pillet, Tauber, arXiv:2204.00440], we establish a number of
general structural results regarding such realizations. In particular, we show
that such a quasi-static process is incompatible with the property of approach
to equilibrium studied in this previous work
Approach to equilibrium in translation-invariant quantum systems: some structural results
We formulate the problem of approach to equilibrium in algebraic quantum
statistical mechanics and study some of its structural aspects, focusing on the
relation between the zeroth law of thermodynamics (approach to equilibrium) and
the second law (increase of entropy). Our main result is that approach to
equilibrium is necessarily accompanied by a strict increase of the specific
(mean) entropy. In the course of our analysis, we introduce the concept of
quantum weak Gibbs state which is of independent interest
Topology in shallow-water waves: a violation of bulk-edge correspondence
We study the two-dimensional rotating shallow-water model describing Earth's
oceanic layers. It is formally analogue to a Schr\"odinger equation where the
tools from topological insulators are relevant. Once regularized at small scale
by an odd-viscous term, such a model has a well-defined bulk topological index.
However, in presence of a sharp boundary, the number of edge modes depends on
the boundary condition, showing an explicit violation of the bulk-edge
correspondence. We study a continuous family of boundary conditions with a rich
phase diagram, and explain the origin of this mismatch. Our approach relies on
scattering theory and Levinson's theorem. The latter does not apply at infinite
momentum because of the analytic structure of the scattering amplitude there,
ultimately responsible for the violation.Comment: 26 pages, 5 figure
The fine structure of heating in a quasiperiodically driven critical quantum system
We study the heating dynamics of a generic one dimensional critical system
when driven quasiperiodically. Specifically, we consider a Fibonacci drive
sequence comprising the Hamiltonian of uniform conformal field theory (CFT)
describing such critical systems and its sine-square deformed counterpart. The
asymptotic dynamics is dictated by the Lyapunov exponent which has a fractal
structure embedding Cantor lines where the exponent is exactly zero. Away from
these Cantor lines, the system typically heats up fast to infinite energy in a
non-ergodic manner where the quasiparticle excitations congregate at a small
number of select spatial locations resulting in a build up of energy at these
points. Periodic dynamics with no heating for physically relevant timescales is
seen in the high frequency regime. As we traverse the fractal region and
approach the Cantor lines, the heating slows enormously and the quasiparticles
completely delocalise at stroboscopic times. Our setup allows us to tune
between fast and ultra-slow heating regimes in integrable systems.Comment: 16 pages, 8 figure
- …