Natural Nonequilibrium States in Quantum Statistical Mechanics

A quantum spin system is discussed where a heat flow between infinite reservoirs takes place in a finite region. A time-dependent force may also be acting. Our analysis is based on a simple technical assumption concerning the time evolution of infinite quantum spin systems. This assumption, physically natural but currently proved for few specific systems only, says that quantum information diffuses in space-time in such a way that the time integral of the commutator of local observables converges: ⁰ _– dt [B, ^t A]<. In this setup one can define a natural nonequilibrium state. In the time-independent case, this nonequilibrium state retains some of the analyticity which characterizes KMS equilibrium states. A linear response formula is also obtained which remains true far from equilibrium. The formalism presented here does not cover situations where (for time-independent forces) the time-translation invariance and uniqueness of the natural nonequilibrium state are broken.     

Analogous negative parity spectra of125Xe and127Xe

The low spin states of the nucleus¹²⁷Xe have been investigated with the (, 2n) reaction by means of in-beam--spectroscopy, using theosiris-cube-spectrometer at the FNTandem accelerator facility of the University of Cologne. In the negative parity system, four excited states for each of the spins 11/2^–.15/2^– and two 5/2^–.9/2^– — states could be established at excitation energies up to 1MeV above the Yrast line. With this new data, we are able to compare the non-Yrast states and their decay properties to the corresponding states of¹²⁵Xe, which had been studied with similar methods in Cologne. The almost one-to-one correspondence between the states of these neighboring neutron-odd nuclei is a clear indication that their excitations at low spin remain collective well above the Yrast line.     

Global C*-Dynamics and Its KMS States of Weakly Inhomogeneous Bipolaronic Superconductors

We establish the limiting dynamics of a class of inhomogeneous bipolaronic models for superconductivity which incorporate deviations from the homogeneous models strong enough to require disjoint representations. The models are of the Hubbard type and the thermodynamics of their homogeneous part has been already elaborated by the authors. Now the dynamics of the systems is evaluated in terms of a generalized perturbation theory and leads to a C*-dynamical system over a classically extended algebra of observables. The classical part of the dynamical system, expressed by a set of 15 nonlinear differential equations, is observed to be independent from the perturbations. The KMS states of the C*-dynamical system are determined on the state space of the extended algebra of observables. The subsimplices of KMS states with unbroken symmetries are investigated and used to define the type of a phase. The KMS phase diagrams are worked out explicitly and compared with the thermodynamic phase structures obtained in the preceding works.     

Spin-dependent photoabsorption at theL-edges of ferromagnetic Gd and Tb metal

The spin-dependent absorption of circularly polarized x-rays is studied at theL-edges of ferromagnetic Gd and Tb metal. At theL ₁-edge a spin-dependent part of the absorption coefficient of 10^–3–10^–2 is observed. Strong resonance absorption known as white line occurs at theL ₂- andL ₃-absorption onset. Correlated with it one finds large spin-dependent absorption effects with amplitudes of a few percent. The spin-dependent absorption spectra reflect the profiles of the spin densities of the states populated in the absorption process. Thep-states show spin densities correlated with the first two flat bands above the Fermi level. The spin density of thed-like states is concentrated in the energy range of the white line. In Gd a splitting of (0.5–0.6) eV of the unoccupied 5d spin up and spin down bands is indicated for both spin-orbit partners. In Tb a large dependence of the 5d spin density on the spin-orbit configuration is observed. The experimental results on the spin densities in Gd are compared with band structure calculations for the ferromagnetic ground-state. The theoretical and experimental spin density profiles agree well for thep-states but not for thed-states. The discrepancy concerning thed-states may be attributed to core-hole polarization effects in the absorption process.     

The first and second nearest neighbour Cr3+ pairs in ruby

The optical spectrum of the exchange coupled first nearest neighbour Cr³⁺ pairs in ruby was studied by absorption, fluorescence and excitation spectroscopy. It was analysed by means of the group theoretical considerations given in part I [1]. The analysis could be verified by measuring the Zeeman effect in fields up to 150 KG. The Zeeman splitting deviates considerably from that of pure spin states even for the orbital singulet of the pair ground state. The exchange integrals of the ground state are found to beJ=–115 cm^–1 andj=–0.7 cm^–1.This work was supported by the Deutsche Forschungsgemeinschaft, SFB 65     

Bose condensation with negative chemical potential

There is widespread prejudice that the existence of Bose-condensed equilibrium states of infinite ideal boson gas requires chemical potential to be strictly zero. This is not true, in general. Using standard techniques of algebraic QFT only, we show that there exists e ^ith invariant extensions T of Schwartz's space D(³) and Bose-condensed KMS states on the CCR algebra (T) for every chemical potential 0 (h=––, the one-particle Hamiltonian). The corresponding condensation fields are, in general, of rapid growth at infinity, with suggested physical implications.     

Supertransferred hyperfine interaction in magnetic insulators (II)

The important mechanisms of supertransferred hyperfine (STHF) interactions in N–O–M chains are briefly discussed: (i) spin polarization ofns states in the N-ion due to the s-d exchange interaction,H _STHF ^sd ; (ii) contributions of spin-polarized states of the intervening O-ion,H _STHF ^II ; (iii) transfer of d-electrons of the M-ion to emptyns states in the N-ion,H _STHF ^III . The dependence ofH _STHF upon the N–O–M bond configuration, electronic structure, and orbital state of the M-ion is presented in a convenient form. The STHF interactions in the chains Sn⁴⁺–O^2––Fe³⁺, Cr³⁺ in compounds with slightly distorted Perovskite structure are considered. The STHF field in the chain Sn⁴⁺–O^2––Cr³⁺ is shown to change the sign within the range of angles near 170°. This conclusion is in line with published data on the isoelectronic chain Sn⁴⁺–O²–Mn⁴⁺ in the compounds Ca_1–x Sr _x MnO₃. The results obtained for the N–O–Fe³⁺ chain are rationalized by the predicted angular dependence ofH _STHF=+ cos + cos². Features of the STHF interactions in N–O–M chains with an M-ion in an orbital degenerate state are examplified by a preliminary analysis of N–O^2––V³⁺ chains in orthovanadites.     

The debye-waller factor in spincrossover molecular crystals: a mössbauer study on [FexZn1−x(ptz)6](BF4)2

In a first approximation the Debye-Waller factor (DWF) of molecular crystals is factorized into a molecular and a lattice part:f=f _m f _l. In the case of spincrossover compounds there is the unique possibility to measure differences of both parts in the two spin states by switching the spin states with the LIESST effect. Measurements of the DWF depending on temperature, -ray direction and spin state were performed with⁵⁷Fe-Mössbauer spectroscopy on three single crystals (R¯3) of the spincrossover system [Fe_xZn_1–x(ptz)₆](BF₄)₂ (ptz=1-propyltetrazole), a concentrated sample withx=1 and diluted ones withx=0.30 andx=0.005. The DWF decreases from 10 to 300 K by a factor of 100 and its anisotropyf _/f increases from 1 to 5.4. The differences of the DWF in the low spin and the high spin state (after LIESST) for the diluted and the concentrated samples were measured at low temperatures ( 50 K). From these data both the Grüneisen constant of the lattice _G=2.9 and the lowest IR active intramolecular frequency (45 cm^–1 (HS), 58 cm^–1 (LS)) have been determined. The contribution of the DWF from the acoustic modes of the lattice is calculated from the elastic constants of rhombohedral [Fe _x Zn_1–x (ptz)₆](BF₄)₂. The contribution of the optical lattice vibrations is estimated. The influence of different DWF in the two spin states on the evaluation of the fraction of molecules in either spin state from Mössbauer area data is discussed.In partial fulfillment of his thesis.     

On the possible temperatures of a dynamical system

A simpleC*-algebra and a continuous one-parameter automorphism group are constructed such that the set of inverse temperatures at which there exist equilibrium states (i.e., KMS states, or, for =±, ground or ceiling states) is an arbitrary closed subset of IR{±}.With partial support of the National Science Foundation     

Statistical mechanics of quantum spin systems. II

In the first part of this paper we continue the general analysis of quantum spin systems. It is demonstrated, for a large class of interactions, that time-translations form a group of automorphisms of theC*-algebra of quasi-local observables and that the thermodynamic equilibrium states are invariant under this group. Further it is shown that the equilibrium states possess the Kubo-Martin-Schwinger analyticity and boundary condition properties. In the second part of the paper we give a general analysis of states which are invariant under space and time translations and also satisfy the KMS boundary condition. A discussion of these latter conditions and their connection with the decomposition of invariant states into ergodic states is given. Various properties pertinent to this discussion are derived.Supported in part by the Office of Naval Research Contract No. Nonr 1866 (5).     

How to avoid “quantum paradoxes”

The theorems showing the impossibility of ascribing to individual quantum systems a definite value of a set of observables, not necessarily commuting,^1–4 are based on the tacit assumption that eachindividual spin component has a discrete dichotomic value. We show explicitly that it is possible to introduce continuous hidden variables for individual spins which avoid these quantum paradoxes without changing any of the observed quantum mechanical results.     

Entanglement evolution of a two-qubit system interacting with a quantum spin environment

We investigate the entanglement dynamics and decoherence of a two-qubit system under a quantum spin environment at finite temperature in the thermodynamics limit. For the case under study, we find different initial states will result in different entanglement evolution, what deserves mentioning here is that the state |Ψ=cosα|01+sinα|10 is most robust than other states when π/2<α<π, since the entanglement remains unchanged or increased under the spin environment. In addition, we also find the anisotropy parameter Δ can suppress the destruction of decoherence induced by the environment, and the undesirable entanglement sudden death arising from the process of entanglement evolution can be efficiently controlled by the inhomogeneous magnetic field ζ.     

Equilibrium Pure States and Nonequilibrium Chaos

We consider nonequilibrium systems such as the Edwards–Anderson Ising spin glass at a temperature where, in equilibrium, there are presumed to be (two or many) broken-symmetry pure states. Following a deep quench, we argue that as time t, although the system is usually in some pure state locally, either it never settles permanently on a fixed length scale into a single pure state, or it does, but then the pure state depends on both the initial spin configuration and the realization of the stochastic dynamics. But this latter case can occur only if there exists an uncountable number of pure states (for each coupling realization) with almost every pair having zero overlap. In both cases, almost no initial spin configuration is in the basin of attraction of a single pure state; that is, the configuration space (resulting from a deep quench) is all boundary (except for a set of measure zero). We prove that the former case holds for deeply quenched 2D ferromagnets. Our results raise the possibility that even if more than one pure state exists for an infinite system, time averages do not necessarily disagree with Boltzmann averages.     

Large Deviations for Quantum Spin Systems

We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages , where the X _i 's are copies of a self-adjoint element X (level one large deviations). From the analyticity of the generating function, we obtain the central limit theorem. We generalize to a level two large deviation principle for the distribution of      

Thermo field dynamics of quantum spin systems

Thermo field dynamics of quantum spin systems is formulated, which gives a new variational principle at finite temperatures. The KMS relation is reformulated as identities among thermal vacuum states. Path integral formulations of the thermal vacuum state are given, which yield a new thermo field Monte Carlo method. Thermo field dynamics of finite-spin systems are studied in detail as simple examples of the present method. Pertubational expansion methods of the thermal state and time-dependent state are also given.     

An algebraic geometry study of theb−c system with arbitrary twist fields and arbitrary statistics

We present an analysis of the generalb–c system (including the – system) on a compact Riemann surface of arbitrary genusg0 by postulating that its correlation functions should only have the singularities imposed by the operator product expansion (OPE) of the system. Studying a very (in fact optimally) general form of theb–c system, we prove rigorously that the standard practice of eliminating zero modes, and even the standard lagrangian, follow from the analyticity structure dictated by the OPE alone. We extend the analysis to consider the most general case of the presence of twist (e.g. spin) fields. We then determine all the possible correlation functions of theb–c system, with statistics unspecified, compatible with the OPE. On imposing Fermi and Bose statistics, we obtain the correlation functions of the fermionicb–c and – systems, respectively.     

Electronic Structure of Immunoactive Molecules of 8–Azagona–12,17–Dione

Using the semiempirical method of partial neglect of differential overlap (PNDO), we have calculated the wave functions, energies, orbital configurations of electronic states, oscillator strengths of transitions, electronic density distributions, and dipole moments for the molecule of biologically active 8–azagona–12,17–dione, containing a conformationally rigid –acyl––aminovinylcarbonyl fragment. It has been established that as to their orbital nature the excited lower and higher singlet electronic states of this molecule are of the n^*– and ^* type respectively. The results of the theoretical analysis are in good qualitative agreement with the spectral data on absorption and luminescence. The calculations of the intermolecular interaction of the compound under consideration with a medium show that the molecular systems under consideration can possess a dynamic multicenter structure.     

Bethe-Salpeter wave functions and transition amplitudes for heavy mesons

The most general form of covariant B-S wave functions and the corresponding integral equations for heavy mesons with arbitrary spin and parity are obtained in the infinite mass limit. A general formula for the I-W functions for transitions between states with arbitrary spin-parity and the ground state is given in terms of these wave functions. Using the covariant instantaneous approximation we apply this formulism to calculate I-W functionsr _1/2,r _3/2 and rates of processes in which a or is emitted in the transitions 1^–0^–, 0⁺0^–, 1⁺1^–.     

Specific Features of Scattering by Spin Fluctuations and the Electronic Structure of Weak Band Semiconducting and Semimetal Magnets

The effect of scattering by spin fluctuations on the electronic structure of weak band semiconducting and semimetal magnets is examined, in particular, the feasibility of origin of the Anderson localized states. The results obtained are analyzed on the example of the FeSi nearly ferromagnetic semiconductor and (FeSi)_1–x (CoSi) _x weak band semimetal magnets with x 0.05.     

The GHS and other correlation inequalities for a class of even ferromagnets

We prove the GHS inequality for families of random variables which arise in certain ferromagnetic models of statistical mechanics and quantum field theory. These include spin –1/2 Ising models, ⁴ field theories, and other continuous spin models. The proofs are based on the properties of a classG ^– of probability measures which contains all measures of the form const exp(–V(x))dx, whereV is even and continuously differentiable anddV/dx is convex on [0, ). A new proof of the GKS inequalities using similar ideas is also given.Supported in part by National Science Foundation Grant MPS 71-02838 A 04.Supported by National Science Foundation Grant MPS 74-24696.Supported in part by National Science Foundation Grant MPS 74-04870.