共查询到20条相似文献,搜索用时 31 毫秒
1.
M. T. Terekhin 《Russian Mathematics (Iz VUZ)》2008,52(6):49-57
We consider a nonlinear system of differential equations in a general case with a singular matrix at the derivatives, with a vector deviation which depends on a parameter. We seek for a periodic solution to the system in the set of trigonometric series such that the sequences of their coefficients belong to the space l 1.We use the method, representing a space as a direct sum of subspaces, and the method of a fixed point of a nonlinear operator as the main investigation techniques.We reduce the question on the existence of a periodic solution to that of the solvability of an operator equation, whose principal part is defined in a finite-dimensional space. 相似文献
2.
We derive, the time-dependent solution of the effective master equation for the reduced density matrix operator of a strongly driven atom coupled to a frequency-tunable cavity and damped by a squeezed vacuum. The effects of different parameters on the entropy squeezing factors, the variance squeezing and population inversion of such an atom emitted from the cavity, are discussed. 相似文献
3.
V. S. Kirchanov 《Theoretical and Mathematical Physics》2006,148(2):1117-1122
For quantum systems with linear dissipation, we obtain the representation of the Linblad equation in the canonical form via
Hermitian operators. Based on this representation, we derive equations for the entropy density and for the statistical projection
operator. We consider the quantum harmonic oscillator with linear dissipation as an example.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 288–294, August, 2006.
An erratum to this article is available at . 相似文献
4.
S. A. Buterin 《Mathematical Notes》2006,80(5-6):631-644
We consider a one-dimensional perturbation of the convolution operator. We study the inverse reconstruction problem for the convolution component using the characteristic numbers under the assumption that the perturbation summand is known a priori. The problem is reduced to the solution of the so-called basic nonlinear integral equation with singularity. We prove the global solvability of this nonlinear equation. On the basis of these results, we prove a uniqueness theorem and obtain necessary and sufficient conditions for the solvability of the inverse problem. 相似文献
5.
Nadaniela Egidi 《Journal of Mathematical Analysis and Applications》2011,377(2):670-682
We consider the integral operator defined on a circular disk, and with kernel the Green function of the Helmholtz operator. We present an analytic framework for the explicit computation of the singular system of this kernel. In particular, the main formulas of this framework are given by a characteristic equation for the singular values and explicit expressions for the corresponding singular functions. We provide also a property of the singular values, that gives an important information for the numerical evaluation of the singular system. Finally, we present a simple numerical experiment, where the singular system computed by a simple implementation of these analytic formulas is compared with the singular system obtained by a discretization of the Green function of the Helmholtz operator. 相似文献
6.
A. M. Sinev 《Theoretical and Mathematical Physics》2009,158(3):377-390
We consider a solvable problem describing the dynamics of a quantum oscillator interacting with an electromagnetic field,
a classical force, and a heat bath. We propose a general method for solving Markovian master equations, the method of quantum
trajectories. We construct the stochastic evolution operator involving the stochastic analogue of the Baker-Hausdorff formula
and calculate the system density matrix for an arbitrary initial state. As a physical application, we evaluate the influence
of the environment at a finite temperature on the accuracy of measuring a weak classical force by the interference method.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 444–459, March, 2009. 相似文献
7.
M. Yakıt Ongun 《中国科学A辑(英文版)》2007,50(2):217-230
In this paper we consider the nonselfadjoint (dissipative) Schrödinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrödinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrödinger boundary value problem are given. 相似文献
8.
We consider a second-order ordinary differential operator with the same spectral parameter in the equation and in one of the boundary conditions. We study the basis property of the system of eigenfunctions of this operator in the space of square summable functions. 相似文献
9.
We consider systems of degenerate differential equations in Banach spaces of a special form. The main instrument of research is the technique of distributions in Banach spaces; namely, the construction of a fundamental operator function introduced by the first author. We translate the results obtained previously for a single equation to the systems of various types and illustrate them with examples. 相似文献
10.
Marianna A. Shubov Miriam Rojas-Arenaza 《Journal of Computational and Applied Mathematics》2010,234(6):1631-126
In this paper, we present a recently developed mathematical model for a short double-wall carbon nanotube. The model is governed by a system of two coupled hyperbolic equations and is reduced to an evolution equation. This equation defines a dissipative semi-group. We show that the semi-group generator is an unbounded nonselfadjoint operator with compact resolvent. Moreover, this operator is a relatively compact perturbation of a certain selfadjoint operator. 相似文献
11.
We consider a model equations describing the coagulation process of a gas on a surface. The problem is modeled by two coupled equations. The first one is a nonlinear transport equation with bilinear coagulation operator while the second one is a nonlinear ordinary differential equation. The velocity and the boundary condition of the transport equation depend on the supersaturation function satisfying the nonlinear ode. We first prove global existence and uniqueness of solution to the nonlinear transport equation then, we consider the coupled problem and prove existence in the large of solutions to the full coagulation system. 相似文献
12.
We consider a model operator acting in a subspace of a Fock space and obtain a symmetrized analogue of the Faddeev equation. For the operator considered, we describe the position and the structure of its essential spectrum.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 3, pp. 544–554, September, 2005. 相似文献
13.
A. M. Chebotarev 《Mathematical Notes》1997,61(4):510-518
We prove that the solution of the Hudson-Parthasarathy quantum stochastic differential equation in the Fock space coincides with the solution of a symmetric boundary value problem for the Schrödinger equation in the interaction representation generated by the energy operator of the environment. The boundary conditions describe the jumps in the phase and the amplitude of the Fourier transforms of the Fock vector components as any of its arguments changes the sign. The corresponding Markov evolution equation (the Lindblad equation or the “master equation”) is derived from the boundary value problem for the Schrödinger equation. 相似文献
14.
M.Yakit ONGUN 《中国科学A辑(英文版)》2007,(2)
In this paper we consider the nonselfadjoint (dissipative) Schrodinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator, and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schrodinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schrodinger boundary value problem are given. 相似文献
15.
A nonconforming domain decomposition approximation for the Helmholtz screen problem with hypersingular operator
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Norbert Heuer Gredy Salmerón 《Numerical Methods for Partial Differential Equations》2017,33(1):125-141
We present and analyze a nonconforming domain decomposition approximation for a hypersingular operator governed by the Helmholtz equation in three dimensions. This operator appears when considering the corresponding Neumann problem in unbounded domains exterior to open surfaces. We consider small wave numbers and low‐order approximations with Nitsche coupling across interfaces. Under appropriate assumptions on mapping properties of the weakly singular and hypersingular operators with Helmholtz kernel, we prove that this method converges almost quasioptimally, that is, with optimal orders reduced by an arbitrarily small positive number. Numerical experiments confirm our error estimate. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 125–141, 2017 相似文献
16.
M.Yakit ONGUN 《中国科学A辑(英文版)》2007,50(2)
In this paper we consider the nonselfadjoint (dissipative) Schr(o)dinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator,and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schr(o)dinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schr(o)dinger boundary value problem are given. 相似文献
17.
V. F. Chistyakov 《Mathematical Notes》2006,80(1-2):109-113
We consider the system of integral equations of the form Ax +V x = Ψ, where V is the Volterra operator with kernel of convolution type and A is a constant matrix, det A = 0. We prove an existence theorem and establish necessary and sufficient conditions for the kernel of the operator of the system to be trivial. 相似文献
18.
Master equations of different types describe the evolution (reduced dynamics) of a subsystem of a larger system generated
by the dynamic of the latter system. Since, in some cases, the (exact) master equations are relatively complicated, there
exist numerous approximations for such equations, which are also called master equations.
In the paper, we develop an exact master equation describing the reduced dynamics of the Wigner function for quantum systems
obtained by a quantization of a Hamiltonian system with a quadratic Hamilton function. First, we consider an exact master
equation for first integrals of ordinary differential equations in infinite-dimensional locally convex spaces. After this,
we apply the results obtained to develop an exact master equation corresponding to a Liouville-type equation (which is the
equation for first integrals of the (system of) Hamilton equation(s)); the latter master equation is called the master Liouville
equation; it is a linear first-order differential equation with respect to a function of real variables taking values in a
space of functions on the phase space. If the Hamilton equation generating the Liouville equation is linear, then the vector
fields that define the first-order linear differential operators in the master Liouville equations are also linear, which
in turn implies that for a Gaussian reference state the Fourier transform of a solution of the master Liouville equation also
satisfies a linear differential equation.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 5, pp. 203–219, 2005. 相似文献
19.
E. V. Vybornyi 《Theoretical and Mathematical Physics》2014,178(1):93-114
We consider the one-dimensional stationary Schrödinger equation with a smooth double-well potential. We obtain a criterion for the double localization of wave functions, exponential splitting of energy levels, and the tunneling transport of a particle in an asymmetric potential and also obtain asymptotic formulas for the energy splitting that generalize the formulas known in the case of a mirror-symmetric potential. We consider the case of higher energy levels and the case of energies close to the potential minimums. We present an example of tunneling transport in an asymmetric double well and also consider the problem of tunnel perturbation of the discrete spectrum of the Schrödinger operator with a single-well potential. Exponentially small perturbations of the energies occur in the case of local potential deformations concentrated only in the classically forbidden region. We also calculate the leading term of the asymptotic expansion of the tunnel perturbation of the spectrum. 相似文献
20.
V. G. Morozov 《Theoretical and Mathematical Physics》2018,194(1):105-113
We propose a systematic approach to the dynamics of open quantum systems in the framework of Zubarev’s nonequilibrium statistical operator method. The approach is based on the relation between ensemble means of the Hubbard operators and the matrix elements of the reduced statistical operator of an open quantum system. This key relation allows deriving master equations for open systems following a scheme conceptually identical to the scheme used to derive kinetic equations for distribution functions. The advantage of the proposed formalism is that some relevant dynamical correlations between an open system and its environment can be taken into account. To illustrate the method, we derive a non-Markovian master equation containing the contribution of nonequilibrium correlations associated with energy conservation. 相似文献