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1.
We present an analytical study of a nonlinear oscillator subject to an additive Ornstein–Uhlenbeck noise. Known results are mainly perturbative and are restricted to the large dissipation limit (obtained by neglecting the inertial term) or to a quasi-white noise (i.e., a noise with vanishingly small correlation time). Here, in contrast, we study the small dissipation case (we retain the inertial term) and consider a noise with finite correlation time. Our analysis is non perturbative and based on a recursive adiabatic elimination scheme a reduced effective Langevin dynamics for the slow action variable is obtained after averaging out the fast angular variable. In the conservative case, we show that the physical observables grow algebraically with time and calculate the associated anomalous scaling exponents and generalized diffusion constants. In the case of small dissipation, we derive an analytic expression of the stationary probability distribution function (PDF) which differs from the canonical Boltzmann–Gibbs distribution. Our results are in excellent agreement with numerical simulations. 相似文献
2.
Molecular dynamics typically incorporates a stochastic-dynamical device, a “thermostat,” in order to drive the system to the
Gibbs (canonical) distribution at a prescribed temperature. When molecular dynamics is used to compute time-dependent properties,
such as autocorrelation functions or diffusion constants, at a given temperature, there is a conflict between the need for
the thermostat to perturb the time evolution of the system as little as possible and the need to establish equilibrium rapidly.
In this article we define a quantity called the “efficiency” of a thermostat which relates the perturbation introduced by
the thermostat to the rate of convergence of average kinetic energy to its equilibrium value. We show how to estimate this
quantity analytically, carrying out the analysis for several thermostats, including the Nosé-Hoover-Langevin thermostat due
to Samoletov et al. (J. Stat. Phys. 128:1321–1336, 2007) and a generalization of the “stochastic velocity rescaling” method suggested by Bussi et al. (J. Chem. Phys. 126:014101,
2007). We find efficiency improvements (proportional to the number of degrees of freedom) for the new schemes compared to Langevin
Dynamics. Numerical experiments are presented which precisely confirm our theoretical estimates. 相似文献
3.
Zhen-Chao Zhu Yu-Qing Zhang An-Min Fu 《International Journal of Theoretical Physics》2011,50(1):308-313
In Deng, Li, and Zhou (Phys. Lett. A 373:399, 2009), the authors propose two improved efficient high-capacity quantum secret sharing schemes to solve the problems existed in
the Letter (Phys. Lett. A 372:1957, 2008), they claim that these two schemes are secure and efficient. However, we point out here that these two improved schemes
are not secure as one agent can obtain all the information without the help from the other agent. We further modify this three-party
quantum secret sharing scheme and make it really secure. In the end, we also give a method to generalize our quantum secret
sharing scheme to arbitrary multi-party scheme. 相似文献
4.
Recently, Dammak and coworkers (Phys. Rev. Lett. 103:190601, 2009) proposed that the quantum statistics of vibrations in condensed systems at low temperature could be simulated by running
molecular dynamics simulations in the presence of a colored noise with an appropriate power spectral density. In the present
contribution, we show how this method can be implemented in a flexible manner and at a low computational cost by synthesizing
the corresponding noise ‘on the fly’. The proposed algorithm is tested for a simple harmonic chain as well as for a more realistic
model of aluminium crystal. The energy and Debye-Waller factor are shown to be in good agreement with those obtained from
harmonic approximations based on the phonon spectrum of the systems. The limitations of the method associated with anharmonic
effects are also briefly discussed. Some perspectives for disordered materials and heat transfer are considered. 相似文献
5.
A Fredholm Determinant Representation in ASEP 总被引:3,自引:2,他引:1
In previous work (Tracy and Widom in Commun. Math. Phys. 279:815–844, 2008) the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice
ℤ. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the
case of step initial condition with particles at the positive integers ℤ+ and consider the distribution function for the mth particle from the left. In Tracy and Widom (Commun. Math. Phys. 279:815–844, 2008) an infinite series of multiple integrals was derived for the distribution. In this note we show that the series can be summed
to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive
(non-rigorously, at this writing) a scaling limit. 相似文献
6.
A simple model for the dynamics of the Magellanic Stream (MS), in the framework of modified gravity models is investigated.
We assume that the galaxy is made up of baryonic matter out of context of dark matter scenario. The model we used here is
named Modified Gravity (MOG) proposed by Moffat (J. Cosmol. Astropart. Phys. 003, 2005). In order to examine the compatibility of the overall properties of the MS under the MOG theory, the observational radial
velocity profile of the MS is compared with the numerical results using the χ
2 fit method. In order to obtain the best model parameters, a maximum likelihood analysis is performed. We also compare the
results of this model with the Cold Dark Matter (CDM) halo model and the other alternative gravity model that proposed by
Bekenstein (Phys. Rev. D 70:083509, 2004), so called TeVeS. We show that by selecting the appropriate values for the free parameters, the MOG theory seems to be plausible
to explain the dynamics of the MS as well as the CDM and the TeVeS models. 相似文献
7.
The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are
studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079–1095, 2009 and The field structure of a vacuum, Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical
Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include
the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations is
developed. The crucial importance of the rest reference systems, with respect to which the dynamics of charged point particles
is framed, is explained and emphasized. A concise expression for the Lorentz force is derived by suitably taking into account
the duality of electromagnetic field and charged particle interactions. Finally, a physical explanation of the vacuum field
medium and its relativistic properties fitting the mathematical framework developed is formulated and discussed. 相似文献
8.
Inflationary models of the early universe provide a natural mechanism for the formation of large scale structure. This success
brings to forefront the question of naturalness: Does a sufficiently long slow roll inflation occur generically or does it
require a careful fine tuning of initial parameters? In recent years there has been considerable controversy on this issue
(Hollands and Wald in Gen Relativ Gravit, 34:2043, 2002; Kofman et al. in J High Energy Phys 10:057, 2002); (Gibbons and Turok in Phys Rev D 77:063516, 2008). In particular, for a quadratic potential, Kofman et al. (J High Energy Phys 10:057, 2002) have argued that the probability of inflation with at least 65 e-foldings is close to one, while Gibbons and Turok (Phys
Rev D 77:063516, 2008) have argued that this probability is suppressed by a factor of ~10−85. We first clarify that such dramatically different predictions can arise because the required measure on the space of solutions
is intrinsically ambiguous in general relativity. We then show that this ambiguity can be naturally resolved in loop quantum
cosmology (LQC) because the big bang is replaced by a big bounce and the bounce surface can be used to introduce the structure
necessary to specify a satisfactory measure. The second goal of the paper is to present a detailed analysis of the inflationary
dynamics of LQC using analytical and numerical methods. By combining this information with the measure on the space of solutions,
we address a sharper question than those investigated in Kofman et al. (J High Energy Phys 10:057, 2002), Gibbons and Turok (Phys Rev D 77:063516, 2008), Ashtekar and Sloan (Phys Lett B 694:108, 2010): What is the probability of a sufficiently long slow roll inflation which is compatible with the seven year WMAP data? We show that the probability is very close to 1. The material is so organized that cosmologists who may be more interested
in the inflationary dynamics in LQC than in the subtleties associated with measures can skip that material without loss of
continuity. 相似文献
9.
Motivated by a recent use of Glauber dynamics for Monte Carlo simulations of path integral representation of quantum spin
models (Krzakala et al. in Phys. Rev. B 78(13):134428, 2008), we analyse a natural Glauber dynamics for the quantum Ising model with a transverse field on a finite graph G. We establish strict monotonicity properties of the equilibrium distribution and we extend (and improve) the censoring inequality
of Peres and Winkler to the quantum setting. Then we consider the case when G is a regular b-ary tree and prove the same fast mixing results established in Martinelli et al. (Commun. Math. Phys. 250(2):301–334, 2004) for the classical Ising model. Our main tool is an inductive relation between conditional marginals (known as the “cavity
equation”) together with sharp bounds on the operator norm of the derivative at the stable fixed point. It is here that the
main difference between the quantum and the classical case appear, as the cavity equation is formulated here in an infinite
dimensional vector space, whereas in the classical case marginals belong to a one-dimensional space. 相似文献
10.
A. Faggionato D. Gabrielli M. Ribezzi Crivellari 《Journal of statistical physics》2009,137(2):259-304
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states (x,σ)∈Ω×Γ, Ω being a region in ℝ
d
or the d-dimensional torus, Γ being a finite set. The continuous variable x follows a piecewise deterministic dynamics, the discrete variable σ evolves by a stochastic jump dynamics and the two resulting evolutions are fully-coupled. We study stationarity, reversibility
and time-reversal symmetries of the process. Increasing the frequency of the σ-jumps, the system behaves asymptotically as deterministic and we investigate the structure of its fluctuations (i.e. deviations
from the asymptotic behavior), recovering in a non Markovian frame results obtained by Bertini et al. (Phys. Rev. Lett. 87(4):040601,
2001; J. Stat. Phys. 107(3–4):635–675, 2002; J. Stat. Mech. P07014, 2007; Preprint available online at , 2008), in the context of Markovian stochastic interacting particle systems. Finally, we discuss a Gallavotti–Cohen-type symmetry
relation with involution map different from time-reversal. 相似文献
11.
We begin with a review and analytical construction of quantum Gaussian process (and quantum Brownian motions) in the sense
of Franz (The Theory of Quantum Levy Processes, [math.PR], 2009), Schürmann (White noise on bioalgebras. Volume 1544 of Lecture Notes in Mathematics. Berlin: Springer-Verlag, 1993) and others, and then formulate and study in details (with a number of interesting examples) a definition of quantum Brownian
motions on those non-commutative manifolds (a la Connes) which are quantum homogeneous spaces of their quantum isometry groups
in the sense of Goswami (Commun Math Phys 285(1):141–160, 2009). We prove that bi-invariant quantum Brownian motion can be ‘deformed’ in a suitable sense. Moreover, we propose a non-commutative
analogue of the well-known asymptotics of the exit time of classical Brownian motion. We explicitly analyze such asymptotics
for a specific example on non-commutative two-torus Aq{\mathcal{A}_\theta} , which seems to behave like a one-dimensional manifold, perhaps reminiscent of the fact that Aq{\mathcal{A}_\theta} is a non-commutative model of the (locally one-dimensional) ‘leaf-space’ of the Kronecker foliation. 相似文献
12.
We study the dynamics of a Fermi gas with a Coulomb interaction potential, and show that, in a mean-field regime, the dynamics
is described by the Hartree-Fock equation. This extends previous work of Bardos et al. [J. Math. Pures Appl. 82(6):665–683,
2003] to the case of unbounded interaction potentials. We also express the mean-field limit as a “superhamiltonian” system, and
state our main result in terms of the Heisenberg-picture dynamics of observables. This is a Egorov-type theorem. 相似文献
13.
C. Bahadoran 《Communications in Mathematical Physics》2012,310(1):1-24
We consider attractive particle systems in
\mathbb Zd{\mathbb {Z}^d} with product invariant measures. We prove that when particles are restricted to a subset of
\mathbb Zd{\mathbb {Z}^d} , with birth and death dynamics at the boundaries, the hydrodynamic limit is given by the unique entropy solution of a conservation
law, with boundary conditions in the sense of Bardos et al. (Comm Part Diff Equ 4:1017–1034, 1979). For the hydrostatic limit between parallel hyperplanes, we prove a multidimensional version of the phase diagram conjectured
in Popkov and Schütz (Europhys Lett 48:257–263, 1999), and show that it is robust with respect to perturbations of the boundaries. 相似文献
14.
Tomasz Schreiber 《Journal of statistical physics》2008,132(4):669-705
We consider polygonal Markov fields originally introduced by Arak and Surgailis (Probab. Theory Relat. Fields 80:543–579,
1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting
contours in the plane, sharing a number of features with the two-dimensional Ising model. We introduce non-homogeneous version
of polygonal fields in anisotropic environment. For these fields we provide a class of new graphical constructions and random
dynamics. These include a generalized dynamic representation, generalized and defective disagreement loop dynamics as well
as a generalized contour birth and death dynamics. Next, we use these constructions as tools to obtain new exact results on
the geometry of higher order correlations of polygonal Markov fields in their consistent regime.
Research supported by the Polish Minister of Science and Higher Education grant N N201 385234 (2008-2010). 相似文献
15.
16.
Yan-Hua Wu Wei-Dong Zhai Wen-Zhen Cao Chong Li 《International Journal of Theoretical Physics》2011,50(2):325-331
We revisited the quantum secure direct communication (QSDC) by using a notation (Li et al. in Phys. Lett. A 297:121, 2002; Li et al. in Int. J. Theor. Phys. 46(7):1815, 2007) and generalized QSDC to arbitrary finite dimensions, we also figured out the decoding formula for QSDC of arbitrary finite
dimensions. In order to overcome the channel noisy, we present a scheme through introduce n auxilians by using quantum swapping. 相似文献
17.
《Physics letters. [Part B]》1999,461(3):183-188
We analyze classical and quantum dynamics of a relativistic particle in 2d spacetimes with constant curvature. We show that global symmetries of spacetime specify the symmetries of physical phase-space and the corresponding quantum theory. To quantize the systems we parametrize the physical phase-space by canonical coordinates. Canonical quantization leads to unitary irreducible representations of SO↑(2.1) group. 相似文献
18.
K. Rasem Qandalji 《International Journal of Theoretical Physics》2009,48(6):1559-1565
In an earlier work we proposed a non-generational conjectural-derivation of all first class constraints (involving, only,
variables compatible with canonical Poisson brackets) for “realistic” gauge (singular) field theories; and we verified the
conjecture in cases of electromagnetic field, Yang-Mills fields interacting with scalar and spinor fields, and the gravitational
field. Here, we will further verify our conjecture for the case of ’t Hooft-Polyakov (HP) monopole’s field (i.e. in the Higgs
vacuum); and show that we will reproduce the results of Qandalji (Int. J. Theor. Phys. 45:1158, 2006), which were reached at using Dirac’s standard multi-generational algorithm. 相似文献
19.
Tom M. Evans Elham Doroodchi Behdad Moghtaderi 《Journal of nanoparticle research》2011,13(9):4395-4396
This brief communication provides a response to Murshed et al. (J Nanopart Res 12:2007–2010, 2010). We acknowledge that three of the equations in our original article (Doroodchi et al. J Nanopart Res 11:1501–1507, 2009) contained minor typographical errors. However, we confirm that these misprinted equations have no bearing on the results
presented within that article. In addition, we would like to clarify that we do not challenge the methodology of Leong et
al. (J Nanopart Res 8:245–254, 2006). Instead, we repeated their analysis using a more general form for the temperature field with continuity imposed across
the particle–nanolayer–liquid interfaces and found that the solution reduces to the Renovated-Maxwell model. 相似文献
20.
In this paper, we investigate Bianchi type-III universe which has dynamical energy density. We introduce three different skewness parameters along spatial directions to quantify the deviation of pressure from isotropy. We also assume that the skewness parameters are time dependent. The Saez-Ballester (J. Phys. Lett. A 113:467, 1986) field equations have been solved by applying a variation law for generalized Hubble’s parameter given by Bermann (Nuovo Cimento B 74:182, 1983). Some physical and kinematical properties of dark energy model are discussed. 相似文献