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1.
We consider a continuous gas with finite range positive pair potential and we assume that the cluster expansion convergence condition holds. We prove a sharp bound on the difference between the finite volume grand canonical and canonical expectation of local observable. The bound is given in terms of the support of the observable, of its grand canonical variance and of the volume on which the system is confined. 相似文献
2.
Tangmei He Jing-bo Yang Hong-wei Tan 《International Journal of Theoretical Physics》2016,55(11):4913-4917
In this paper, we present a grand canonical ensemble interpretation for the massive charged particles tunneling from a charged black hole. The probability distribution function corresponding the emission shell system is derived in details, and the expression is same as the tunneling rate in Parikh-Wilzeck framework. With this result, the statistical significance of the quantum tunneling radiation is discussed. 相似文献
3.
We investigate thermodynamics of the (2 1)-dimensional AdS black hole in grand canonical ensemble. In the York‘s formalism, the black hole is enclosed in a “box“ with a finite radius and the boundary temperature, radius and potential are fixed in the grand canonical ensemble. We investigate the thermodynamical properties such as action,entropy, temperature, etc. We only find the stable solution for (2 1)-dimensional AdS black hole and do not find the instanton with the negative heat capacity.`` 相似文献
4.
Grand Canonical Ensemble Monte Carlo Simulation of Depletion Interactions in Colloidal Suspensions 下载免费PDF全文
Depletion interactions in colloidal suspensions confined between two parallel plates are investigated by using acceptance ratio method with grand canonical ensemble Monte Carlo simulation. The numerical results show that both the depletion potential and depletion force are affected by the confinement from the two parallel plates. Furthermore, it is found that in the grand canonical ensemble Monte Carlo simulation, the depletion interactions are strongly affected by the generalized chemical potential. 相似文献
5.
We investigate thermodynamics of
the (2+1)-dimensional AdS black hole in grand canonical ensemble. In the York's formalism, the black hole is
enclosed in a “box” with a finite radius and the boundary temperature,
radius and potential are fixed in the grand canonical ensemble. We investigate the thermodynamical properties such as action, entropy, temperature, etc. We only find the stable solution for (2+1)-dimensional AdS black hole and do not find the instanton with the negative heat capacity. 相似文献
6.
Supersymmetry is formulated within a functional approach of euclidean quantum field theory. The rǒle of the euclidean Lie superalgebra and its relation to the Poincaré Lie superalgebra are investigated in detail. As example we study the Wess-Zumino model in two dimensions. 相似文献
7.
Elena Pulvirenti Dimitrios Tsagkarogiannis 《Communications in Mathematical Physics》2012,316(2):289-306
We consider a system of particles confined in a box ${\Lambda \subset \mathbb{R}^d}$ interacting via a tempered and stable pair potential. We prove the validity of the cluster expansion for the canonical partition function in the high temperature - low density regime. The convergence is uniform in the volume and in the thermodynamic limit it reproduces Mayer??s virial expansion providing an alternative and more direct derivation which avoids the deep combinatorial issues present in the original proof. 相似文献
8.
Garnet Kin-Lic Chan Paul W. Ayers Ernest S. Croot III 《Journal of statistical physics》2002,109(1-2):289-299
Using physical arguments and partition theoretic methods, we demonstrate under general conditions, that the eigenvalues w(m) of the grand canonical density matrix decay rapidly with their index m, like w(m)exp[–B
–1(ln m)1+1/
], where B and are positive constants, O(1), which may be computed from the spectrum of the Hamiltonian. We compute values of B and for several physical models, and confirm our theoretical predictions with numerical experiments. Our results have implications in a variety of questions, including the behaviour of fluctuations in ensembles, and the convergence of numerical density matrix renormalization group techniques. 相似文献
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10.
Horia D. Cornean 《Communications in Mathematical Physics》2000,212(1):1-27
Consider a charged Bose gas without self-interactions, confined in a three dimensional cubic box of side L S 1 and subjected to a constant magnetic field B p 0. If the bulk density of particles A and the temperature T are fixed, then define the canonical magnetization as the partial derivative with respect to B of the reduced free energy. Our main result is that it admits thermodynamic limit for all strictly positive A, T and B. It is also proven that the canonical and grand canonical magnetizations (the last one at fixed average density) are equal up to the surface order corrections. 相似文献
11.
We develop a formalism for general relativistic, grand canonical ensembles in space-times with timelike Killing fields. Using
that, we derive ideal gas laws, and show how they depend on the geometry of the particular space-times. A systematic method
for calculating Newtonian limits is given for a class of these space-times, which is illustrated for Kerr space-time. In addition,
we prove uniqueness of the infinite volume Gibbs measure, and absence of phase transitions for a class of interaction potentials
in anti-de Sitter space. 相似文献
12.
In this paper a new proof of an identity of Giacomin, Olla, and Spohn is given. The identity relates the 2 point correlation function of a Euclidean field theory to the expectation of the Green's function for a pde with random coefficients. The Euclidean field theory is assumed to have convex potential. An inequality of Brascamp and Lieb therefore implies Gaussian bounds on the Fourier transform of the 2 point correlation function. By an application of results from random pde, the previously mentioned identity implies pointwise Gaussian bounds on the 2 point correlation function. 相似文献
13.
Journal of Statistical Physics - In this note we study the block spin mean-field Potts model, in which the spins are divided into s blocks and can take $$qge 2$$ different values (colors). Each... 相似文献
14.
Marius Costeniuc Richard S. Ellis Hugo Touchette Bruce Turkington 《Journal of statistical physics》2005,119(5-6):1283-1329
This paper shows for a general class of statistical mechanical models that when the microcanonical and canonical ensembles are nonequivalent on a subset of values of the energy, there often exists a generalized canonical ensemble that satisfies a strong form of equivalence with the microcanonical ensemble that we call universal equivalence. The generalized canonical ensemble that we consider is obtained from the standard canonical ensemble by adding an exponential factor involving a continuous function g of the Hamiltonian. For example, if the microcanonical entropy is C2, then universal equivalence of ensembles holds with g taken from a class of quadratic functions, giving rise to a generalized canonical ensemble known in the literature as the Gaussian ensemble. This use of functions g to obtain ensemble equivalence is a counterpart to the use of penalty functions and augmented Lagrangians in global optimization. linebreak Generalizing the paper by Ellis et al. [J. Stat. Phys. 101:999–1064 (2000)], we analyze the equivalence of the microcanonical and generalized canonical ensembles both at the level of equilibrium macrostates and at the thermodynamic level. A neat but not quite precise statement of one of our main results is that the microcanonical and generalized canonical ensembles are equivalent at the level of equilibrium macrostates if and only if they are equivalent at the thermodynamic level, which is the case if and only if the generalized microcanonical entropy s–g is concave. This generalizes the work of Ellis et al., who basically proved that the microcanonical and canonical ensembles are equivalent at the level of equilibrium macrostates if and only if they are equivalent at the thermodynamic level, which is the case if and only if the microcanonical entropy s is concave. 相似文献
15.
We prove that, for low-temperature systems considered in the Pirogov-Sinai theory, uniqueness in the class of translation-periodic
Gibbs states implies global uniqueness, i.e. the absence of any non-periodic Gibbs state. The approach to this infinite volume
state is exponentially fast.
Received: 4 June 1996 / Accepted: 30 October 1996 相似文献
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17.
Myron W. Evans 《Foundations of Physics Letters》2003,16(6):513-547
A generally covariant wave equation is derived geometrically for grand unified field theory. The equation states most generally that the covariant d'Alembertian acting on the vielbein vanishes for the four fields which are thought to exist in nature: gravitation, electromagnetism, weak field and strong field. The various known field equations are derived from the wave equation when the vielbein is the eigenfunction. When the wave equation is applied to gravitation the wave equation is the eigenequation of wave mechanics corresponding to Einstein's field equation in classical mechanics, the vielbein eigenfunction playing the role of the quantized gravitational field. The three Newton laws, Newton's law of universal gravitation, and the Poisson equation are recovered in the classical and nonrelativistic, weak-field limits of the quantized gravitational field. The single particle wave-equation and Klein-Gordon equations are recovered in the relativistic, weak-field limit of the wave equation when scalar components are considered of the vielbein eigenfunction of the quantized gravitational field. The Schrödinger equation is recovered in the non-relativistec, weak-field limit of the Klein-Gordon equation). The Dirac equation is recovered in this weak-field limit of the quantized gravitational field (the nonrelativistic limit of the relativistic, quantezed gravitational field when the vielbein plays the role of the spinor. The wave and field equations of O(3) electrodynamics are recovered when the vielbein becomes the relativistic dreibein (triad) eigenfunction whose three orthonormal space indices become identified with the three complex circular indices (1), (2), (3), and whose four spacetime indices are the indices of non-Euclidean spacetime (the base manifold). This dreibein is the potential dreibein of the O(3) electromagnetic field (an electromagnetic potential four-vector for each index (1), (2), (3)). The wave equation of the parity violating weak field is recovered when the orthonormal space indices of the relativistic dreibein eigenfunction are identified with the indices of the three massive weak field bosons. The wave equation of the strong field is recovered when the orthonormal space indices of the relativistic vielbein eigenfunction become the eight indices defined by the group generators of the SU (3) group. 相似文献
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19.
We revisit the expansion recently proposed by Pulvirenti and Tsagkarogiannis for a system of N continuous particles in the Canonical Ensemble. Under the sole assumption that the particles interact via a tempered and stable pair potential and are subjected to the usual free boundary conditions, we show the analyticity of the Helmholtz free energy at low densities and, using the Penrose tree graph identity, we establish a lower bound for the convergence radius which happens to be identical to the lower bound of the convergence radius of the virial series in the Grand Canonical ensemble established by Lebowitz and Penrose in 1964. We also show that the free energy can be written as a series in powers of the density whose k-th order coefficient coincides, modulo terms o(N)/N, with the k-th order virial coefficient divided by k+1, according to its expression in terms of the m-th order (with m≤k+1) simply connected cluster integrals first given by Mayer in 1942. We finally give an upper bound for the k-th order virial coefficient which slightly improves, at high temperatures, the bound obtained by Lebowitz and Penrose. 相似文献
20.
Singular and supersingular finite rank perturbations of self-adjoint operators are studied using methods from renormalization theory for quantum fields. It is shown that the ideas from dimensional and Pauli–Villars regulatizations can be applied to determine uniquely certain finite rank supersingular perturbations. Approach is based on the regularization of homogeneous singular quadratic forms. 相似文献