1,172 research outputs found
Path Integral for Quantum Operations
In this paper we consider a phase space path integral for general
time-dependent quantum operations, not necessarily unitary. We obtain the path
integral for a completely positive quantum operation satisfied Lindblad
equation (quantum Markovian master equation). We consider the path integral for
quantum operation with a simple infinitesimal generator.Comment: 24 pages, LaTe
Fractional Derivative as Fractional Power of Derivative
Definitions of fractional derivatives as fractional powers of derivative
operators are suggested. The Taylor series and Fourier series are used to
define fractional power of self-adjoint derivative operator. The Fourier
integrals and Weyl quantization procedure are applied to derive the definition
of fractional derivative operator. Fractional generalization of concept of
stability is considered.Comment: 20 pages, LaTe
Phase-Space Metric for Non-Hamiltonian Systems
We consider an invariant skew-symmetric phase-space metric for
non-Hamiltonian systems. We say that the metric is an invariant if the metric
tensor field is an integral of motion. We derive the time-dependent
skew-symmetric phase-space metric that satisfies the Jacobi identity. The
example of non-Hamiltonian systems with linear friction term is considered.Comment: 12 page
Metal-insulator transition in a two-dimensional electron system: the orbital effect of in-plane magnetic field
The conductance of an open quench-disordered two-dimensional (2D) electron
system subject to an in-plane magnetic field is calculated within the framework
of conventional Fermi liquid theory applied to actually a three-dimensional
system of spinless electrons confined to a highly anisotropic (planar)
near-surface potential well. Using the calculation method suggested in this
paper, the magnetic field piercing a finite range of infinitely long system of
carriers is treated as introducing the additional highly non-local scatterer
which separates the circuit thus modelled into three parts -- the system as
such and two perfect leads. The transverse quantization spectrum of the inner
part of the electron waveguide thus constructed can be effectively tuned by
means of the magnetic field, even though the least transverse dimension of the
waveguide is small compared to the magnetic length. The initially finite
(metallic) value of the conductance, which is attributed to the existence of
extended modes of the transverse quantization, decreases rapidly as the
magnetic field grows. This decrease is due to the mode number reduction effect
produced by the magnetic field. The closing of the last current-carrying mode,
which is slightly sensitive to the disorder level, is suggested as the origin
of the magnetic-field-driven metal-to-insulator transition widely observed in
2D systems.Comment: 19 pages, 7 eps figures, the extension of cond-mat/040613
Fractional Systems and Fractional Bogoliubov Hierarchy Equations
We consider the fractional generalizations of the phase volume, volume
element and Poisson brackets. These generalizations lead us to the fractional
analog of the phase space. We consider systems on this fractional phase space
and fractional analogs of the Hamilton equations. The fractional generalization
of the average value is suggested. The fractional analogs of the Bogoliubov
hierarchy equations are derived from the fractional Liouville equation. We
define the fractional reduced distribution functions. The fractional analog of
the Vlasov equation and the Debye radius are considered.Comment: 12 page
"Unusual" metals in two dimensions: one-particle model of the metal-insulator transition at T=0
The conductance of disordered nano-wires at T=0 is calculated in one-particle
approximation by reducing the original multi-dimensional problem for an open
bounded system to a set of exactly one-dimensional non-Hermitian problems for
mode propagators. Regarding two-dimensional conductor as a limiting case of
three-dimensional disordered quantum waveguide, the metallic ground state is
shown to result from its multi-modeness. On thinning the waveguide (in
practice, e. g., by means of the ``pressing'' external electric field) the
electron system undergoes a continuous phase transition from metallic to
insulating state. The result predicted conform qualitatively to the observed
anomalies of the resistance of different planar electron and hole systems.Comment: 7 pages, LATEX-2
Continuous Limit of Discrete Systems with Long-Range Interaction
Discrete systems with long-range interactions are considered. Continuous
medium models as continuous limit of discrete chain system are defined.
Long-range interactions of chain elements that give the fractional equations
for the medium model are discussed. The chain equations of motion with
long-range interaction are mapped into the continuum equation with the Riesz
fractional derivative. We formulate the consistent definition of continuous
limit for the systems with long-range interactions. In this paper, we consider
a wide class of long-range interactions that give fractional medium equations
in the continuous limit. The power-law interaction is a special case of this
class.Comment: 23 pages, LaTe
On the Bethe Ansatz for the Jaynes-Cummings-Gaudin model
We investigate the quantum Jaynes-Cummings model - a particular case of the
Gaudin model with one of the spins being infinite. Starting from the Bethe
equations we derive Baxter's equation and from it a closed set of equations for
the eigenvalues of the commuting Hamiltonians. A scalar product in the
separated variables representation is found for which the commuting
Hamiltonians are Hermitian. In the semi classical limit the Bethe roots
accumulate on very specific curves in the complex plane. We give the equation
of these curves. They build up a system of cuts modeling the spectral curve as
a two sheeted cover of the complex plane. Finally, we extend some of these
results to the XXX Heisenberg spin chain.Comment: 16 page
A Complete Version of the Glauber Theory for Elementary Atom - Target Atom Scattering and Its Approximations
A general formalism of the Glauber theory for elementary atom (EA) - target
atom (TA) scattering is developed. A second-order approximation of its complete
version is considered in the framework of the optical-model perturbative
approach. A `potential' approximation of a second-order optical model is
formulated neglecting the excitation effects of the TA. Its accuracy is
evaluated within the second-order approximation for the complete version of the
Glauber EA-TA scattering theory.Comment: PDFLaTeX, 10 pages, no figures; an updated versio
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