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1.
Within the general framework ofC*-algebra approach to mathematical foundation of statistical mechanics, we prove a theorem which gives a natural explanation for the appearance of the chemical potential (as a thermodynamical parameter labelling equilibrium states) in the presence of a symmetry (under gauge transformations of the first kind). As a symmetry, we consider a compact abelian groupG acting as *-automorphisms of aC*-algebra (quasi-local field algebra) and commuting (elementwise) with the time translation automorphisms t of . Under a technical assumption which is satisfied by examples of physical interest, we prove that the set of all extremal t -KMS states (pure phases) ofG-fixed-point subalgebra (quasi-local observable algebra) of satisfying a certain faithfulness condition is in one-to-one correspondence with the set of all extremalG-invariant t · t -KMS states of with varying over one-parameter subgroups ofG (the specification of being the specification of the chemical potential), where the correspondence is that the restriction of to is .  相似文献   

2.
Let denote the conformally invariant neutral free scalar field on ×S n. The naive lightcone Hamiltonian for a p interaction is given by cp, where C denotes a lightcone in ×S n, and the Wick power is relative to the free vacuum. We show that this sesquilinear form annihilates the free vacuum if n3 is odd, p>2, and p(n–1)0 mod 4.  相似文献   

3.
LetS() be the group of finite permutations on countably many symbols. We exhibit an embedding ofS() into a UHF-algebra of Glimm typen such that, if is a *-derivation vanishing onS() and satisfying °=0, where is the unique trace on , then admits an extension which is the generator of aC*-dynamics.Work supported in part by NSF  相似文献   

4.
Detailed calculations of far infrared absorption in ultrafine metallic particles are reported. Effective medium treatments of the composite of particles and their surrounding are carried out within the Maxwell Garnett and Bruggeman theories. Generalizations of these to encompass dipole-dipole interaction and oxide pellicles are discussed. The dielectric permeability of the particles is specified either by the Drude (D) model with a size limited mean free path, or by the quantum mechanical derivation of Gor'kov and Éliashberg (GE). Excepting narrow diameter (x) and frequency ( ) intervals the absorption coefficients can be approximated by =fCx , wheref is the filling factor (taken to be small),C is a constant which depends on the free electron parameters, and and are integers. Results for largerfs are included also. The magnitudes ofC, and differ in general for the Drude and Gor'kov-Éliashberg theories; they are also different forxx C , wherex D C 5 nm andx GE C is typically 20 nm. The quantityx c signifies a transition from a range where is dominated by the dielectric polarisation to one where the magnetic polarisation is largest. An interesting multiple peak structure is found from detailed calculations of GE vs. for sufficiently small identical particles. Effects of log-normal size distributions are derived explicitely; any fine structure in the GE vs.x functions is found to be completely washed out for practically attainable distribution widths.Work at Cornell University was supported by the National Science Foundation through the Materials Science CenterWork at Chalmers University of Technology was supported by the Swedish Natural Science Research Council  相似文献   

5.
Let (x) be the Dirac's delta,q(x)L 1 (R)L 2 (R) be a real valued function, and , R; we will consider the following class of one-dimensional formal Schrödinger operators on . It is known that to the formal operator may be associated a selfadjoint operatorH(,) onL 2(R). Ifq is of finite range, for >0 and || is small enough, we prove thatH(,) has an antibound state; that is the resolvent ofH(,) has a pole on the negative real axis on the second Riemann sheet.Work done while the author was supported by an undergraduate fellowship of the (Italian) National Research Council (CNR).  相似文献   

6.
For automorphism groups of operator algebras we show how properties of the difference t – ' t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if t – 't 0.28 for smallt, then = 0(+)°-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference t – ' t =O(t) ast ; 0, then = + and if t – ' t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC 0,C 0 * groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation  相似文献   

7.
The paper studies unbounded symmetric and dissipative implementations (S,G) of*-superderivations ofC *-algebras . It associates with them representations S of the domainsD() of on the deficiency spacesN(S) of the symmetric operatorsS. A link is obtained between the deficiency indicesn ±(S) ofS and the dimensions of irreducible representations of . For the case when (S,G) is a maximal implementation and max(n ±(S))<, some conditions are given for the representation S to be semisimple and to extend to a bounded representation of .  相似文献   

8.
Let be the Jacobi matrix associated with polynomialT(z) of degreeN2. The spectrum of is the Julia set associated withT(z) which in many cases is a Cantor set. Let (1) denote the result of omitting the first row and column ofJ. Then it is shown that the spectrum of (1) may be purely discrete.It is also shown that forT(z)= NCN(z/) for > , whereC N is a Chebychev polynomial the coefficients of and (1) are limit periodic extending the work of Bellissard, Bessis, and Moussa (Phys. Rev. Lett.49, 701–704 (1982)).Supported in part by N.S.F. grant DMS-8401609Supported in part by N.S.F. grant MCS-8203325  相似文献   

9.
Consider the electrical resistancer n (p) of a hypercubic bond lattice [O,n] d inZ d , where the bonds have resistance 1 with probabilityp or with probability 1-p. Letp n (p)=n 2-d r n (p) andp(p)=limnpn(p). It is well known thatp(p)< ifp>p c andp(p)= ifp<p c , wherep c is the percolation threshold. Here we show thatp(p c )=, and .  相似文献   

10.
Couch and Torrence suggest that the vacuum Einstein equations admit a larger class of asymptotically flat solutions than those exhibiting the peeling property. Starting with the assumption that , (d/dr) and (/x A ) , wherex A (A = 2, 3) are angular coordinates, they show that , where 1 2 and 1<0; , where 2 1 and 1< 1; and 4 and 3 peel as they would under the stronger peeling conditions. The Winicour-Tamburino energy-momentun and angular momentum integrals for these solutions, in general, diverge. In fact, since Couch and Torrence determine only the radial dependence of the solution, it is not clear that the solutions are well defined. We find that the stronger assumption , (d/dr) , and (/x A ) does result in well-defined solutions for which both the energy-momentum and angular momentum intergrals are not only finite but result in the same expressions as are obtained for peeling space-times. This assumption appears to be the minimal assumption that is necessary for investigating outgoing radiation at null infinity.In part based on a dissertation by Stephanie Novak and submitted to Syracuse University in partial fulfillment of the requirement for the Ph.D. degree.  相似文献   

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