365 research outputs found
Quantum wire junctions breaking time reversal invariance
We explore the possibility to break time reversal invariance at the junction
of quantum wires. The universal features in the bulk of the wires are described
by the anyon Luttinger liquid. A simple necessary and sufficient condition for
the breaking of time reversal invariance is formulated in terms of the
scattering matrix at the junction. The phase diagram of a junction with generic
number of wires is investigated in this framework. We give an explicit
classification of those critical points which can be reached by bosonization
and study the interplay between their stability and symmetry content.Comment: Extended version (Appendices C and D and some references added, typos
corrected) to appear in Phys. Rev.
Spectral theorem for the Lindblad equation for quadratic open fermionic systems
The spectral theorem is proven for the quantum dynamics of quadratic open
systems of n fermions described by the Lindblad equation. Invariant eigenspaces
of the many-body Liouvillean dynamics and their largest Jordan blocks are
explicitly constructed for all eigenvalues. For eigenvalue zero we describe an
algebraic procedure for constructing (possibly higher dimensional) spaces of
(degenerate) non-equilibrium steady states.Comment: 19 pages, no figure
Looking for a time independent Hamiltonian of a dynamical system
In this paper we introduce a method for finding a time independent
Hamiltonian of a given dynamical system by canonoid transformation. We also
find a condition that the system should satisfy to have an equivalent time
independent formulation. We study the example of damped oscillator and give the
new time independent Hamiltonian for it, which has the property of tending to
the standard Hamiltonian of the harmonic oscillator as damping goes to zero.Comment: Some references added, LATEX fixing
Soliton solutions of the Kadomtsev-Petviashvili II equation
We study a general class of line-soliton solutions of the
Kadomtsev-Petviashvili II (KPII) equation by investigating the Wronskian form
of its tau-function. We show that, in addition to previously known line-soliton
solutions, this class also contains a large variety of new multi-soliton
solutions, many of which exhibit nontrivial spatial interaction patterns. We
also show that, in general, such solutions consist of unequal numbers of
incoming and outgoing line solitons. From the asymptotic analysis of the
tau-function, we explicitly characterize the incoming and outgoing
line-solitons of this class of solutions. We illustrate these results by
discussing several examples.Comment: 28 pages, 4 figure
Majorana spinors and extended Lorentz symmetry in four-dimensional theory
An extended local Lorentz symmetry in four-dimensional (4D) theory is
considered. A source of this symmetry is a group of general linear
transformations of four-component Majorana spinors GL(4,M) which is isomorphic
to GL(4,R) and is the covering of an extended Lorentz group in a 6D Minkowski
space M(3,3) including superluminal and scaling transformations. Physical
space-time is assumed to be a 4D pseudo-Riemannian manifold. To connect the
extended Lorentz symmetry in the M(3,3) space with the physical space-time, a
fiber bundle over the 4D manifold is introduced with M(3,3) as a typical fiber.
The action is constructed which is invariant with respect to both general 4D
coordinate and local GL(4,M) spinor transformations. The components of the
metric on the 6D fiber are expressed in terms of the 4D pseudo-Riemannian
metric and two extra complex fields: 4D vector and scalar ones. These extra
fields describe in the general case massive particles interacting with an extra
U(1) gauge field and weakly interacting with ordinary particles, i.e.
possessing properties of invisible (dark) matter.Comment: 24 page
Geometric phase around exceptional points
A wave function picks up, in addition to the dynamic phase, the geometric
(Berry) phase when traversing adiabatically a closed cycle in parameter space.
We develop a general multidimensional theory of the geometric phase for
(double) cycles around exceptional degeneracies in non-Hermitian Hamiltonians.
We show that the geometric phase is exactly for symmetric complex
Hamiltonians of arbitrary dimension and for nonsymmetric non-Hermitian
Hamiltonians of dimension 2. For nonsymmetric non-Hermitian Hamiltonians of
higher dimension, the geometric phase tends to for small cycles and
changes as the cycle size and shape are varied. We find explicitly the leading
asymptotic term of this dependence, and describe it in terms of interaction of
different energy levels.Comment: 4 pages, 1 figure, with revisions in the introduction and conclusio
Commutator Relations Reveal Solvable Structures in Unambiguous State Discrimination
We present a criterion, based on three commutator relations, that allows to
decide whether two self-adjoint matrices with non-overlapping support are
simultaneously unitarily similar to quasidiagonal matrices, i.e., whether they
can be simultaneously brought into a diagonal structure with 2x2-dimensional
blocks. Application of this criterion to unambiguous state discrimination
provides a systematic test whether the given problem is reducible to a solvable
structure. As an example, we discuss unambiguous state comparison.Comment: 5 pages, discussion of related work adde
Young diagrams and N-soliton solutions of the KP equation
We consider -soliton solutions of the KP equation,
(-4u_t+u_{xxx}+6uu_x)_x+3u_{yy}=0 . An -soliton solution is a solution
which has the same set of line soliton solutions in both
asymptotics and . The -soliton solutions include
all possible resonant interactions among those line solitons. We then classify
those -soliton solutions by defining a pair of -numbers with , which labels line solitons in the solution. The
classification is related to the Schubert decomposition of the Grassmann
manifolds Gr, where the solution of the KP equation is defined as a
torus orbit. Then the interaction pattern of -soliton solution can be
described by the pair of Young diagrams associated with . We also show that -soliton solutions of the KdV equation obtained by
the constraint cannot have resonant interaction.Comment: 22 pages, 5 figures, some minor corrections and added one section on
the KdV N-soliton solution
Gravitational field of relativistic gyratons
The metric ansatz is used to describe the gravitational field of a beam-pulse
of spinning radiation (gyraton) in an arbitrary number of spacetime dimensions
D. First we demonstrate that this metric belongs to the class of metrics for
which all scalar invariants constructed from the curvature and its covariant
derivatives vanish. Next, it is shown that the vacuum Einstein equations reduce
to two linear problems in (D-2)-dimensional Euclidean space. The first is to
find the static magnetic potential created by a point-like source. The second
requires finding the electric potential created by a point-like source
surrounded by given distribution of the electric charge. To obtain a generic
gyraton-type solution of the vacuum Einstein equations it is sufficient to
allow the coefficients in the corresponding harmonic decompositions of
solutions of the linear problems to depend arbitrarily on retarded time and
substitute the obtained expressions in the metric ansatz. We discuss properties
of the solutions for relativistic gyratons and consider special examples.Comment: 11 page
Lagrangian Framework for Systems Composed of High-Loss and Lossless Components
Using a Lagrangian mechanics approach, we construct a framework to study the
dissipative properties of systems composed of two components one of which is
highly lossy and the other is lossless. We have shown in our previous work that
for such a composite system the modes split into two distinct classes,
high-loss and low-loss, according to their dissipative behavior. A principal
result of this paper is that for any such dissipative Lagrangian system, with
losses accounted by a Rayleigh dissipative function, a rather universal
phenomenon occurs, namely, selective overdamping: The high-loss modes are all
overdamped, i.e., non-oscillatory, as are an equal number of low-loss modes,
but the rest of the low-loss modes remain oscillatory each with an extremely
high quality factor that actually increases as the loss of the lossy component
increases. We prove this result using a new time dynamical characterization of
overdamping in terms of a virial theorem for dissipative systems and the
breaking of an equipartition of energy.Comment: 53 pages, 1 figure; Revision of our original manuscript to
incorporate suggestions from refere
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