28 research outputs found
Phase-space approach to Berry's phases
We propose a new formula for the adiabatic Berry phase which is based on
phase-space formulation of quantum mechanics. This approach sheds a new light
into the correspondence between classical and quantum adiabatic phases -- both
phases are related with the averaging procedure: Hannay's angle with averaging
over the classical torus and Berry's phase with averaging over the entire
classical phase space with respect to the corresponding Wigner function.
Generalizations to the non-abelian Wilczek--Zee case and mixed states are also
included.Comment: 5 page
Non-Markovian quantum dynamics: local versus non-local
We analyze non-Markovian evolution of open quantum systems. It is shown that
any dynamical map representing evolution of such a system may be described
either by non-local master equation with memory kernel or equivalently by
equation which is local in time. These two descriptions are complementary: if
one is simple the other is quite involved, or even singular, and vice versa.
The price one pays for the local approach is that the corresponding generator
keeps the memory about the starting point `t_0'. This is the very essence of
non-Markovianity. Interestingly, this generator might be highly singular,
nevertheless, the corresponding dynamics is perfectly regular. Remarkably,
singularities of generator may lead to interesting physical phenomena like
revival of coherence or sudden death and revival of entanglement.Comment: 4.5 pages; new examples are adde
Generation of a dipole moment by external field in Born-Infeld non-linear electrodynamics
The mechanism for the generation of a dipole moment due to an external field
is presented for the Born-Infeld charged particle. The 'polarizability
coefficient' is calculated: it is proportional to the third power of the
characteristic length in the Born-Infeld theory. Some physical implications are
briefly discussed.Comment: 8 pages, LATE
On the structure of entanglement witnesses and new class of positive indecomposable maps
We construct a new class of positive indecomposable maps in the algebra of 'd
x d' complex matrices. Each map is uniquely characterized by a cyclic
bistochastic matrix. This class generalizes a Choi map for d=3. It provides a
new reach family of indecomposable entanglement witnesses which define
important tool for investigating quantum entanglement.Comment: 18 page
General form of quantum evolution
We propose a complete treatment of a local in time dynamics of open quantum
systems. In this approach Markovian evolution turns out to be a special case of
a general non-Markovian one. We provide a general representation of the local
generator which generalizes well known Lindblad representation for the
Markovian dynamics. It shows that the structure of non-Markovian generators is
highly intricate and the problem of their classification is still open. Simple
examples illustrate our approach.Comment: 4 page
From Markovian semigroup to non-Markovian quantum evolution
We provided a class of legitimate memory kernels leading to completely
positive trace preserving dynamical maps. Our construction is based on a simple
normalization procedure. Interestingly, when applied to the celebrated
Wigner-Weisskopf theory it gives the standard Markovian evolution governed by
the local master equation.Comment: 8 page
Symmetry witnesses
A symmetry witness is a suitable subset of the space of selfadjoint trace
class operators that allows one to determine whether a linear map is a symmetry
transformation, in the sense of Wigner. More precisely, such a set is invariant
with respect to an injective densely defined linear operator in the Banach
space of selfadjoint trace class operators (if and) only if this operator is a
symmetry transformation. According to a linear version of Wigner's theorem, the
set of pure states, the rank-one projections, is a symmetry witness. We show
that an analogous result holds for the set of projections with a fixed rank
(with some mild constraint on this rank, in the finite-dimensional case). It
turns out that this result provides a complete classification of the set of
projections with a fixed rank that are symmetry witnesses. These particular
symmetry witnesses are projectable; i.e., reasoning in terms of quantum states,
the sets of uniform density operators of corresponding fixed rank are symmetry
witnesses too.Comment: 15 page
Memory in a nonlocally damped oscillator
We analyze the new equation of motion for the damped oscillator. It differs
from the standard one by a damping term which is nonlocal in time and hence it
gives rise to a system with memory. Both classical and quantum analysis is
performed. The characteristic feature of this nonlocal system is that it breaks
local composition low for the classical Hamiltonian dynamics and the
corresponding quantum propagator.Comment: minor corrections added; title change