446 research outputs found
PT-symmetric quantum Liouvillian dynamics
We discuss a combination of unitary and anti-unitary symmetry of quantum
Liouvillian dynamics, in the context of open quantum systems, which implies a
D2 symmetry of the complex Liovillean spectrum. For sufficiently weak
system-bath coupling it implies a uniform decay rate for all coherences, i.e.
off-diagonal elements of the system's density matrix taken in the eigenbasis of
the Hamiltonian. As an example we discuss symmetrically boundary driven open
XXZ spin 1/2 chains.Comment: Note [18] added with respect to a published version, explaining the
symmetry of the matrix V [eq. (14)
Explicit solution of the Lindblad equation for nearly isotropic boundary driven XY spin 1/2 chain
Explicit solution for the 2-point correlation function in a non-equilibrium
steady state of a nearly isotropic boundary-driven open XY spin 1/2 chain in
the Lindblad formulation is provided. A non-equilibrium quantum phase
transition from exponentially decaying correlations to long-range order is
discussed analytically. In the regime of long-range order a new phenomenon of
correlation resonances is reported, where the correlation response of the
system is unusually high for certain discrete values of the external bulk
parameter, e.g. the magnetic field.Comment: 20 Pages, 5 figure
Third quantization
The basic ideas of second quantization and Fock space are extended to density
operator states, used in treatments of open many-body systems. This can be done
for fermions and bosons. While the former only requires the use of a
non-orthogonal basis, the latter requires the introduction of a dual set of
spaces. In both cases an operator algebra closely resembling the canonical one
is developed and used to define the dual sets of bases. We here concentrated on
the bosonic case where the unboundedness of the operators requires the
definitions of dual spaces to support the pair of bases. Some applications,
mainly to non-equilibrium steady states, will be mentioned.Comment: To appear in the Proceedings of Symposium Symmetries in Nature in
memoriam Marcos Moshinsky.
http://www.cicc.unam.mx/activities/2010/SymmetriesInNature/index.htm
Parametric statistics of zeros of Husimi representations of quantum chaotic eigenstates and random polynomials
Local parametric statistics of zeros of Husimi representations of quantum
eigenstates are introduced. It is conjectured that for a classically fully
chaotic systems one should use the model of parametric statistics of complex
roots of Gaussian random polynomials which is exactly solvable as demonstrated
below. For example, the velocities (derivatives of zeros of Husimi function
with respect to an external parameter) are predicted to obey a universal
(non-Maxwellian) distribution where is the mean square velocity. The
conjecture is demonstrated numerically in a generic chaotic system with two
degrees of freedom. Dynamical formulation of the ``zero-flow'' in terms of an
integrable many-body dynamical system is given as well.Comment: 13 pages in plain Latex (1 figure available upon request
Quantization over boson operator spaces
The framework of third quantization - canonical quantization in the Liouville
space - is developed for open many-body bosonic systems. We show how to
diagonalize the quantum Liouvillean for an arbitrary quadratic n-boson
Hamiltonian with arbitrary linear Lindblad couplings to the baths and, as an
example, explicitly work out a general case of a single boson.Comment: 9 pages, no figure
Markovian kinetic equation approach to electron transport through quantum dot coupled to superconducting leads
We present a derivation of Markovian master equation for the out of
equilibrium quantum dot connected to two superconducting reservoirs, which are
described by the Bogoliubov-de Gennes Hamiltonians and have the chemical
potentials, the temperatures, and the complex order parameters as the relevant
quantities. We consider a specific example in which the quantum dot is
represented by the Anderson impurity model and study the transport properties,
proximity effect and Andreev bound states in equilibrium and far from
equilibrium setups.Comment: 10 pages, 6 figure
Integration over matrix spaces with unique invariant measures
We present a method to calculate integrals over monomials of matrix elements
with invariant measures in terms of Wick contractions. The method gives exact
results for monomials of low order. For higher--order monomials, it leads to an
error of order 1/N^alpha where N is the dimension of the matrix and where alpha
is independent of the degree of the monomial. We give a lower bound on the
integer alpha and show how alpha can be increased systematically. The method is
particularly suited for symbolic computer calculation. Explicit results are
given for O(N), U(N) and for the circular orthogonal ensemble.Comment: 12 pages in revtex, no figure
On general relation between quantum ergodicity and fidelity of quantum dynamics
General relation is derived which expresses the fidelity of quantum dynamics,
measuring the stability of time evolution to small static variation in the
hamiltonian, in terms of ergodicity of an observable generating the
perturbation as defined by its time correlation function. Fidelity for ergodic
dynamics is predicted to decay exponentially on time-scale proportional to
delta^(-2) where delta is the strength of perturbation, whereas faster,
typically gaussian decay on shorter time scale proportional to delta^(-1) is
predicted for integrable, or generally non-ergodic dynamics. This surprising
result is demonstrated in quantum Ising spin-1/2 chain periodically kicked with
a tilted magnetic field where we find finite parameter-space regions of
non-ergodic and non-integrable motion in thermodynamic limit.Comment: Slightly revised version, 4.5 RevTeX pages, 2 figure
Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
We calculate a nonequilibrium steady state of a quantum XX chain in the
presence of dephasing and driving due to baths at chain ends. The obtained
state is exact in the limit of weak driving while the expressions for one- and
two-point correlations are exact for an arbitrary driving strength. In the
steady state the magnetization profile and the spin current display diffusive
behavior. Spin-spin correlation function on the other hand has long-range
correlations which though decay to zero in either the thermodynamical limit or
for equilibrium driving. At zero dephasing a nonequilibrium phase transition
occurs from a ballistic transport having short-range correlations to a
diffusive transport with long-range correlations.Comment: 5 page
Theory of quantum Loschmidt echoes
In this paper we review our recent work on the theoretical approach to
quantum Loschmidt echoes, i.e. various properties of the so called echo
dynamics -- the composition of forward and backward time evolutions generated
by two slightly different Hamiltonians, such as the state autocorrelation
function (fidelity) and the purity of a reduced density matrix traced over a
subsystem (purity fidelity). Our main theoretical result is a linear response
formalism, expressing the fidelity and purity fidelity in terms of integrated
time autocorrelation function of the generator of the perturbation.
Surprisingly, this relation predicts that the decay of fidelity is the slower
the faster the decay of correlations. In particular for a static
(time-independent) perturbation, and for non-ergodic and non-mixing dynamics
where asymptotic decay of correlations is absent, a qualitatively different and
faster decay of fidelity is predicted on a time scale 1/delta as opposed to
mixing dynamics where the fidelity is found to decay exponentially on a
time-scale 1/delta^2, where delta is a strength of perturbation. A detailed
discussion of a semi-classical regime of small effective values of Planck
constant is given where classical correlation functions can be used to predict
quantum fidelity decay. Note that the correct and intuitively expected
classical stability behavior is recovered in the classical limit, as the
perturbation and classical limits do not commute. The theoretical results are
demonstrated numerically for two models, the quantized kicked top and the
multi-level Jaynes Cummings model. Our method can for example be applied to the
stability analysis of quantum computation and quantum information processing.Comment: 29 pages, 11 figures ; Maribor 2002 proceeding
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