116 research outputs found
Transient regime in non-linear transport through many-level quantum dots
We investigate the nonstationary electronic transport in noninteracting
nanostructures driven by a finite bias and time-dependent signals applied at
their contacts to the leads. The systems are modelled by a tight-binding
Hamiltonian and the transient currents are computed from the non-equilibrium
Green-Keldysh formalism. The numerical implementation is not restricted to weak
coupling to the leads and does not imply the wide-band limit assumption for the
spectral width of the leads. As an application of the method we study in detail
the transient behavior and the charge dynamics in single and double quantum
dots connected to leads by a step-like potential, but the method allows as well
the consideration of non-periodic potentials or short pulses. We show that when
the higher energy levels of the isolated system are located within the bias
window of the leads the transient current approaches the steady state in a
non-oscillatory smooth fashion. At moderate coupling to the leads and fixed
bias the transient acquires a step-like structure, the length of the steps
increasing with the system size. The number of levels inside a finite bias
window can be tuned by a constant gate potential. We find also that the
transient behavior depends on the specific way of coupling the leads to the
mesoscopic system.Comment: RevTeX, 12 pages, 11 include .eps figure
A microscopic model for Josephson currents
A microscopic model of a Josephson junction between two superconducting
plates is proposed and analysed. For this model, the nonequilibrium steady
state of the total system is explicitly constructed and its properties are
analysed. In particular, the Josephson current is rigorously computed as a
function of the phase difference of the two plates and the typical properties
of the Josephson current are recovered
Conversion of a general quantum stabilizer code to an entanglement distillation protocol
We show how to convert a quantum stabilizer code to a one-way or two-way
entanglement distillation protocol. The proposed conversion method is a
generalization of those of Shor-Preskill and Nielsen-Chuang. The recurrence
protocol and the quantum privacy amplification protocol are equivalent to the
protocols converted from [[2,1]] stabilizer codes. We also give an example of a
two-way protocol converted from a stabilizer better than the recurrence
protocol and the quantum privacy amplification protocol. The distillable
entanglement by the class of one-way protocols converted from stabilizer codes
for a certain class of states is equal to or greater than the achievable rate
of stabilizer codes over the channel corresponding to the distilled state, and
they can distill asymptotically more entanglement from a very noisy Werner
state than the hashing protocol.Comment: LaTeX2e, 18 pages, 1 figure. Version 4 added an example of two-way
protocols better than the recurrence protocol and the quantum privacy
amplification protocol. Version 2 added the quantum privacy amplification
protocol as an example converted from a stabilizer code, and corrected many
errors. Results unchanged from V
Hjelmslev Geometry of Mutually Unbiased Bases
The basic combinatorial properties of a complete set of mutually unbiased
bases (MUBs) of a q-dimensional Hilbert space H\_q, q = p^r with p being a
prime and r a positive integer, are shown to be qualitatively mimicked by the
configuration of points lying on a proper conic in a projective Hjelmslev plane
defined over a Galois ring of characteristic p^2 and rank r. The q vectors of a
basis of H\_q correspond to the q points of a (so-called) neighbour class and
the q+1 MUBs answer to the total number of (pairwise disjoint) neighbour
classes on the conic.Comment: 4 pages, 1 figure; extended list of references, figure made more
illustrative and in colour; v3 - one more figure and section added, paper
made easier to follow, references update
Adiabatic non-equilibrium steady states in the partition free approach
Consider a small sample coupled to a finite number of leads, and assume that
the total (continuous) system is at thermal equilibrium in the remote past. We
construct a non-equilibrium steady state (NESS) by adiabatically turning on an
electrical bias between the leads. The main mathematical challenge is to show
that certain adiabatic wave operators exist, and to identify their strong limit
when the adiabatic parameter tends to zero. Our NESS is different from, though
closely related with the NESS provided by the Jak{\v s}i{\'c}-Pillet-Ruelle
approach. Thus we partly settle a question asked by Caroli {\it et al} in 1971
regarding the (non)equivalence between the partitioned and partition-free
approaches
Exact solution of Markovian master equations for quadratic fermi systems: thermal baths, open XY spin chains, and non-equilibrium phase transition
We generalize the method of third quantization to a unified exact treatment
of Redfield and Lindblad master equations for open quadratic systems of n
fermions in terms of diagonalization of 4n x 4n matrix. Non-equilibrium thermal
driving in terms of the Redfield equation is analyzed in detail. We explain how
to compute all physically relevant quantities, such as non-equilibrium
expectation values of local observables, various entropies or information
measures, or time evolution and properties of relaxation. We also discuss how
to exactly treat explicitly time dependent problems. The general formalism is
then applied to study a thermally driven open XY spin 1/2 chain. We find that
recently proposed non-equilibrium quantum phase transition in the open XY chain
survives the thermal driving within the Redfield model. In particular, the
phase of long-range magnetic correlations can be characterized by
hypersensitivity of the non-equilibrium-steady state to external (bath or bulk)
parameters. Studying the heat transport we find negative thermal conductance
for sufficiently strong thermal driving, as well as non-monotonic dependence of
the heat current on the strength of the bath coupling.Comment: 24 pages, 12 figures, submitted to New Journal of Physics, Focus
issue "Quantum Information and Many-Body Theory
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
Octonionic representations of Clifford algebras and triality
The theory of representations of Clifford algebras is extended to employ the
division algebra of the octonions or Cayley numbers. In particular, questions
that arise from the non-associativity and non-commutativity of this division
algebra are answered. Octonionic representations for Clifford algebras lead to
a notion of octonionic spinors and are used to give octonionic representations
of the respective orthogonal groups. Finally, the triality automorphisms are
shown to exhibit a manifest \perm_3 \times SO(8) structure in this framework.Comment: 33 page
Third quantization: a general method to solve master equations for quadratic open Fermi systems
The Lindblad master equation for an arbitrary quadratic system of n fermions
is solved explicitly in terms of diagonalization of a 4n x 4n matrix, provided
that all Lindblad bath operators are linear in the fermionic variables. The
method is applied to the explicit construction of non-equilibrium steady states
and the calculation of asymptotic relaxation rates in the far from equilibrium
problem of heat and spin transport in a nearest neighbor Heisenberg XY spin 1/2
chain in a transverse magnetic field.Comment: 24 pages, with 8 eps figures - few minor corrections to the published
version, e.g. anti-symmetrizing the matrix given by eq. (27
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