196 research outputs found
Time-dependent quantum transport: causal superfermions, exact fermion-parity protected decay mode, and Pauli exclusion principle for mixed quantum states
We extend the recently developed causal superfermion approach to the
real-time transport theory to time-dependent decay problems.Its usefulness is
illustrated for the Anderson model of a quantum dot with tunneling rates
depending on spin due to the ferromagnetic electrodes and/or spin polarization
of the tunnel junction. We set up a second quantization scheme for density
operators in the Liouville-Fock space constructing causal field superoperators
using the fundamental physical principles of causality/probability conservation
and the fermion-parity superselection (univalence). The time-dependent
perturbation series for the time-evolution is renormalized by explicitly
performing the wide-band limit on the superoperator level. The short and
long-time reservoir correlations are shown to be tightly linked to the
occurrence of causal field destruction and creation superoperators,
respectively. The effective theory takes as a reference a damped local system,
providing an interesting starting point for numerical calculations of memory
kernels in real-time. A remarkable feature of this approach is the natural
appearance of a measurable fermion-parity protected decay mode. It already can
be calculated exactly in the Markovian, infinite temperature limit by leading
order perturbation theory, yet persists unaltered for the finite temperature,
interaction and tunneling spin polarization. Furthermore, we show how a
Liouville-space analog of the Pauli principle directly leads to the exact
result in the noninteracting limit: surprisingly, it is obtained in finite
(second) order renormalized perturbation theory, both for the self-energy as
well as the time-evolution propagator. For this limit we calculate the
time-evolution of the full density operator starting from an arbitrary initial
state on the quantum dot, including spin and pairing coherences and
two-particle correlations.Comment: This version contains the more extensive introduction and the
conclusion, discussing an experimental relevance of the obtained exact result
for the new decay mode. A lot of new references have been added. The more
detailed comparison of the results obtained for the noninteracting case with
the known results has been done. Small typos have been fixe
Symmetries and Paraparticles as a Motivation for Structuralism
This paper develops an analogy proposed by Stachel between general relativity
(GR) and quantum mechanics (QM) as regards permutation invariance. Our main
idea is to overcome Pooley's criticism of the analogy by appeal to
paraparticles.
In GR the equations are (the solution space is) invariant under
diffeomorphisms permuting spacetime points. Similarly, in QM the equations are
invariant under particle permutations. Stachel argued that this feature--a
theory's `not caring which point, or particle, is which'--supported a
structuralist ontology.
Pooley criticizes this analogy: in QM the (anti-)symmetrization of fermions
and bosons implies that each individual state (solution) is fixed by each
permutation, while in GR a diffeomorphism yields in general a distinct, albeit
isomorphic, solution.
We define various versions of structuralism, and go on to formulate Stachel's
and Pooley's positions, admittedly in our own terms. We then reply to Pooley.
Though he is right about fermions and bosons, QM equally allows more general
types of symmetry, in which states (vectors, rays or density operators) are not
fixed by all permutations (called `paraparticle states'). Thus Stachel's
analogy is revived.Comment: 45 pages, Latex, 3 Figures; forthcoming in British Journal for the
Philosophy of Scienc
Five approaches to exact open-system dynamics: Complete positivity, divisibility and time-dependent observables
To extend the classical concept of Markovianity to an open quantum system,
different notions of the divisibility of its dynamics have been introduced.
Here we analyze this issue by five complementary approaches: equations of
motion, real-time diagrammatics, Kraus-operator sums, as well as time-local
(TCL) and nonlocal (Nakajima-Zwanzig) quantum master equations. As a case study
featuring several types of divisible dynamics, we examine in detail an exactly
solvable noninteracting fermionic resonant level coupled arbitrarily strongly
to a fermionic bath at arbitrary temperature in the wideband limit. In
particular, the impact of divisibility on the time-dependence of the observable
level occupation is investigated and compared with typical Markovian
approximations. We find that the loss of semigroup-divisibility is accompanied
by a prominent reentrant behavior: Counter to intuition, the level occupation
may temporarily \emph{increase} significantly in order to reach a stationary
state with \emph{smaller} occupation, implying a reversal of the measurable
transport current. In contrast, the loss of the so-called completely-positive
divisibility is more subtly signaled by the \emph{prohibition} of such current
reversals in specific time-intervals. Experimentally, it can be detected in the
family of transient currents obtained by varying the initial occupation. To
quantify the nonzero footprint left by the system in its effective environment,
we determine the exact time-dependent state of the latter as well as related
information measures such as entropy, exchange entropy and coherent
information.Comment: Submitted to The Journal of Chemical Physics, 19 pages + 14 pages of
appendices with 13 figures. Significantly extended introduction and
discussion, no results change
Algebraic conformal quantum field theory in perspective
Conformal quantum field theory is reviewed in the perspective of Axiomatic,
notably Algebraic QFT. This theory is particularly developped in two spacetime
dimensions, where many rigorous constructions are possible, as well as some
complete classifications. The structural insights, analytical methods and
constructive tools are expected to be useful also for four-dimensional QFT.Comment: Review paper, 40 pages. v2: minor changes and references added, so as
to match published versio
Fermionic systems for quantum information people
The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity superselection in the fermionic case on the other. We discuss these two fundamental differences extensively, and illustrate these through the Jordan-Wigner representation in a coherent, self-contained, pedagogical way, from the point of view of quantum information theory. Our perspective leads us to develop some useful new tools for the treatment of fermionic systems, such as the fermionic (quasi-)tensor product, fermionic canonical embedding, fermionic partial trace, fermionic products of maps and fermionic embeddings of maps. We formulate these by direct, easily applicable formulas, without mode permutations, for arbitrary partitionings of the modes. It is also shown that fermionic reduced states can be calculated by the fermionic partial trace, containing the proper phase factors. We also consider variants of the notions of fermionic mode correlation and entanglement, which can be endowed with the usual, local operation based motivation, if the fermion number parity superselection rule is imposed. We also elucidate some other fundamental points, related to joint map extensions, which make the parity superselection inevitable in the description of fermionic systems
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