On the equilibrium states in quantum statistical mechanics

Representations of theC*-algebra of observables corresponding to thermal equilibrium of a system at given temperatureT and chemical potential are studied. Both for finite and for infinite systems it is shown that the representation is reducible and that there exists a conjugation in the representation space, which maps the von Neumann algebra spanned by the representative of onto its commutant. This means that there is an equivalent anti-linear representation of in the commutant. The relation of these properties with the Kubo-Martin-Schwinger boundary condition is discussed.     

Ellipsoidal bag model for heavy quark system

The ellipsoidal bag model is used to describe heavy quark systems such asQ ,Q g andQ ² . Instead of two step model, these states are described by an uniform picture. The potential derived from the ellipsoidal bag forQ is almost equivalent to the Cornell potential. For aQ ² system with large quark pair separation, an improvement of 70 MeV is obtained comparing with the spherical bag.     

Landau Hamiltonians with Unbounded Random Potentials

We prove the almost sure existence of a pure point spectrum for the two-dimensional Landau Hamiltonian with an unbounded Anderson-like random potential, provided that the magnetic field is sufficiently large. For these models, the probability distribution of the coupling constant is assumed to be absolutely continuous. The corresponding densityg has support equal to , and satisfies , for some > 0. This includes the case of Gaussian distributions. We show that the almost sure spectrum is , provided the magnetic field B0. We prove that for each positive integer n, there exists a field strength B _n , such that for all B>B _n , the almost sure spectrum is pure point at all energies except in intervals of width about each lower Landau level , for m < n. We also prove that for any B0, the integrated density of states is Lipschitz continuous away from the Landau energiesE _n (B). This follows from a new Wegner estimate for the finite-area magnetic Hamiltonians with random potentials.     

On the reconstruction of a unitary matrix from its moduli

We study the problem of reconstructing a unitary matrix from the knowledge of the moduli of its matrix elements, first in the case of a symmetric matrix, which could be theS matrix forn coupled channels, second in the case of a non-symmetric matrix like the Cabibbo-Kobayashi-Maskawa matrix forn generations of quarks and leptons. In the symmetric case we find conditions under which the problem has solutions differing in a non-trivial way, but also situations where one has continuous ambiguities.In the non-symmetric case we show that forn>3 there may be continuous ambiguities, of which we give an exhaustic list forn=4. We give indications that there is also a set of moduli for which one has discrete solutions, but no rigorous proof.Unité associée au CNRS n^o 040768     

D-mesons in dense nuclear matter

The D-meson properties in dense nuclear matter are studied. The D-meson spectral density is obtained within the framework of a coupled-channel self-consistent calculation, assuming as bare meson-baryon interaction a separable potential. The resonance is generated dynamically in our coupled-channel model. The medium modifications of the D-meson properties due to Pauli blocking and the dressing of D-mesons, nucleons and pions are also studied. We conclude that the self-consistent coupled-channel process reduces the in-medium effects on the D-meson compared to previous literature which did not consider the coupled-channel structure.Received: 14 January 2005, Published online: 31 May 2005PACS: 14.40.Lb, 14.20.Gk, 21.65. + f     

Logarithmic Sobolev inequality for lattice gases with mixing conditions

Let denote the grand canonical Gibbs measure of a lattice gas in a cube of sizeL with the chemical potential and a fixed boundary condition. Let be the corresponding canonical measure defined by conditioning on . Consider the lattice gas dynamics for which each particle performs random walk with rates depending on near-by particles. The rates are chosen such that, for everyn andL fixed, is a reversible measure. Suppose that the Dobrushin-Shlosman mixing conditions holds for forall chemical potentials . We prove that for any probability densityf with respect to ; here the constant is independent ofn orL andD denotes the Dirichlet form of the dynamics. The dependence onL is optimal.Research partially supported by U.S. National Science Foundations grant 9403462, Sloan Foundation Fellowship and David and Lucile Packard Foundation Fellowship.     

The imaginary part of the local potential equivalent to the non-local α-nucleus optical potential

A simple expression of the α-nucleus optical potential has been derived from the Feshbach formula by using a closure approximation for summing over the excited states of the target nucleus. It has been shown that the correction to the real folding model potential is small. The imaginary local potential equivalent to the non-local Feshbach potential has been studied in detail for Ca nuclei and shown to reproduce quite well the gross properties of empirical potentials above 100 MeV with, however, a lack of absorption in the surface region. The A-dependence of the imaginary potential volume integral has also been investigated.     

On the parametrisation of unitary matrices by the moduli of their elements

The parametrisation of ann×n unitary matrix by the moduli of its elements is not a well posed problem, i.e. there are continuous and discrete ambiguities which naturally appear. We show that the continuous ambiguity is (n–1)(n–3)-dimensional in the general case and in the symmetric caseS _ij=S_ij. We give also lower bounds on the number of discrete ambiguities, the number of solutions being at least in the first case and for the symmetric one, where [r] denotes the integral part ofr.     

Coordinates of the quantum plane as q-tensor operators in (\mathfrak{s}\mathfrak{u}(2)*\mathfrak{s}\mathfrak{u}(2))

The relation between the set of transformations of the quantum plane and the quantum universal enveloping algebra U _q (u(2)) is investigated by constructing representations of the factor algebra U _q (u(2))* . The noncommuting coordinates of , on which U _q (2) * U _q (2) acts, are realized as q-spinors with respect to each U _q (u(2)) algebra. The representation matrices of U _q (2) are constructed as polynomials in these spinor components. This construction allows a derivation of the commutation relations of the noncommuting coordinates of directly from properties of U _q (u(2)). The generalization of these results to U _q (u(n)) and is also discussed.     

On fixing the scale in QCD from lattice calculations

Recent results of lattice Monte-Carlo calculations in QCD are used to estimate the value of . Special attention is paid to the role played by the light quarks in the construction of the continuum limit in QCD. The resulting value of turns out to be strongly dependent onn _f , the number of light quarks taken into account.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.On leave of absence from theInstitute of Physics, Czechosl. Accd. Sci., Na Slovance 2, 180 40 Praha 8, Czechoslovakia.     

Exact Wave Functions of Time-Dependent Hamiltonian Systems Involving Quadratic, Inverse Quadratic, and (1/\hat x)\hat p + \hat p(1/\hat x) Terms

We use the dynamical invariant method to derive quantum-mechanical solution of time-dependent Hamiltonian system consisting quadratic potential, inverse quadratic potential, and . The term in Hamiltonian containing gives the expression such as in coordinate space, which we can often meet in radial equation of quantum many body problem. The wave functions differed only a time-dependent phase factor from the eigenstates of the invariant operator Î and expressed in terms of an associated Laguerre function.     

New quantum groups by double-bosonisation

We obtain new family of quasitriangular Hopf algebras via the author's recent double-bosonisation construction for new quantum groups. They are versions of U _q(su _n+1) with a fermionic rather than bosonic quantum plane of roots adjoined to U _q(su _n). We give the n = 2 case in detail. We also consider the anyonic-double of an anyonic ( ) braided group and the double-bosonisation of the free braided group in n variables.     

N=2 structures on solvable Lie algebras: Thec=9 classification

Let be a finite-dimensional Lie algebra (not necessarily semisimple). It is known that if is self-dual (that is, if it possesses an invariant metric) then it admits anN=1 (affine) Sugawara construction. Under certain additional hypotheses, thisN=1 structure admits anN=2 extension. If this is the case, is said to possess anN=2 structure. It is also known that anN=2 structure on a self-dual Lie algebra is equivalent to a vector space decomposition , where are isotropic Lie subalgebras. In other words,N=2 structures on in one-to-one correspondence with Manin triples . In this paper we exploit this correspondence to obtain a classification of thec=9N=2 structures on solvable Lie algebras. In the process we also give some simple proofs for a variety of Lie algebras. In the process we also give some simple proofs for a variety of Lie algebraic results concerning self-dual Lie algebras admitting symplectic or Kähler structures.     

Transport Properties of Kicked and Quasiperiodic Hamiltonians

We study transport properties of Schrödinger operators depending on one or more parameters. Examples include the kicked rotor and operators with quasi-periodic potentials. We show that the mean growth exponent of the kinetic energy in the kicked rotor and of the mean square displacement in quasiperiodic potentials is generically equal to 2: this means that the motion remains ballistic, at least in a weak sense, even away from the resonances of the models. Stronger results are obtained for a class of tight-binding Hamiltonians with an electric field E(t) = E ₀+ E ₁cos t. For with 3/2)$$ " align="middle" border="0"> we show that the mean square displacement satisfies for suitable choices of , E ₀, and E ₁. We relate this behavior to the spectral properties of the Floquet operator of the problem.     

Binary reactions in $$\bar pp$$ collisions at intermediate energies

We discuss here the binary reactions of strange and charmed particle production in collisions at intermediate energies. In the case of baryon production with only one strange or charmed quark the cross section is determined by planar diagrams withK ^*,K ^** orD ^*,D ^**-meson poles in thet-channel. We calculated these diagrams in the frame of quark-gluon string model (QGSM) proposed earlier. We obtained also the cross-sections for reactions with baryon exchange in thet-channel with and pair in the final state. Predicted cross-sections for the reactions of production are of the order of hundred nanobarns. Using reggeon calculus we estimated cross-sections of binary reactions with two or three strange quarks in the final state: and . We discuss also the possible manifestation of color transparency effects in reactions with antiprotons on nuclei where all antiproton quarks annihilate.     

Control on arrangement of AgI clusters incorporated into zeolite LTA

AgI clusters were incorporated into Li, Na, and K-form LTA zeolites with a loading number of four AgI molecules per -cage. The X-ray powder diffraction (XRD) patterns and optical absorption spectra of the samples were obtained. The XRD patterns indicate that the sizes of the clusters and their arrangements depend on the type of alkali-cations. AgI clusters with different sizes, i.e., (AgI)_n and (AgI)_8–n (5n7), are arrayed alternatively in Na-form LTA conforming to the space group of P2₁3. AgI-loaded Li-form LTA also conformed to the space group of P2₁3, although (AgI)_n clusters seem to be distributed disorderly. On the contrary, (AgI)₄ cluster is in each cage in K-form LTA conforming to the space group of or . The optical spectra showed that Li and Na-form LTAs include (AgI)_n (5 n), and that K-form LTA includes (AgI)₄ cluster in each cage.     

Functional Relations in Stokes Multipliers—Fun with x6+αx2 Potential

We consider eigenvalue problems in quantum mechanics in one dimension. Hamiltonians contain a class of double well potential terms, x +x , for example. The space coordinate is continued to a complex plane and the connection problem of fundamental system of solutions is considered. A hidden U ( (2 1)) structure arises in fusion relations of Stokes multipliers. With this observation, we derive coupled nonlinear integral equations which characterize the spectral properties of both ± potentials simultaneously.     

On the Gibbsian Nature of the Random Field Kac Model Under Block-Averaging

We consider the Kac–Ising model in an arbitrary configuration of local magnetic fields = , in any dimension d, at any inverse temperature. We investigate the Gibbs properties of the 'renormalized' infinite volume measures obtained by block averaging any of the Gibbs-measures corresponding to fixed , with block-length small enough compared to the range of the Kac-interaction. We show that these measures are Gibbs measures for the same renormalized interaction potential. This potential depends locally on the field configuration and decays exponentially, uniformly in , for which we give explicit bounds. The construction of the potential is based on a high temperature-type cluster expansion.     

Evidence for a new Hume-Rothery phase with an amorphous structure

It will be shown that binary amorphous alloys with a noble metal and a polyvalent non-transition element, as constituents, can be described essentially as a Hume-Rothery phase. Some structural as well as transport properties depend on , the average number of the conduction electrons per atom. A strong similarity between the amorphous and the corresponding liquid alloys was found. Alloys of the type mentioned can exist in a homogeneous amorphous phase within a concentration range which is limited on the noble-metal rich side by =1.8 and on the other side by about 20 at% noble-metal content. The influence of the conduction electrons, manifested in the Friedel oscillations of the effective pair potentials, is responsible for structural and electronic transport properties. For amorphous and liquid alloys with =1.8 it is interesting to note thatk _pe , the wave number at which the maximum in the structure factor occurs, is equal to 2k _F , the diameter of the Fermi sphere. As far as we have determined, all amorphous alloys with =1.8 containing the same noble metal have the same crystallization temperature and the same Hall coefficient independent of the polyvalent element. The individual influence of the polyvalent constituents can only be seen with increasing .     

Spectral decomposition of path space in solvable lattice model

We give thespectral decomposition of the path space of the vertex model with respect to the local energy functions. The result suggests the hidden Yangian module structure on the levell integrable modules, which is consistent with the earlier work [1] in the level one case. Also we prove the fermionic character formula of the levell integrable representations in consequence.