Local transformations and KMS states

A unified approach to the DLR and KMS conditions is presented emphasizing local properties.     

On the existence of KMS states

A necessary and sufficient condition for the existence of KMS states is formulated in terms of a certain left ideal in the algebraA ⁰ A.     

KMS states for the Weyl algebra

We consider the possible automorphism groups for the Weyl algebra overR, resp.T, and classify those for which KMS states, unique or not unique, exist.     

Passive states and KMS states for general quantum systems

We characterize equilibrium states of quantum systems by a condition of passivity suggested by the second principle of thermodynamics. Ground states and -KMS states for all inverse temperatures 0 are completely passive. We prove that these states are the only completely passive ones. For the special case of states describing pure phases, assuming the passivity we reproduce the results of Haag et al.     

Existence of ground states and KMS states for approximately inner dynamics

A strongly continuous one parameter group of *-automorphisms of aC*-algebra with unit is said to be approximately inner if it can be approximated strongly by inner one parameter groups of *-automorphisms. It is shown that an approximately inner one parameter group of *-automorphisms has a ground state and, if there exists a trace state, a KMS state for all inverse temperatures. It follows that quantum lattice systems have ground states and KMS states. Conditions that a strongly continuous one parameter group of *-automorphisms of a UHF algebra be approximately inner are given in terms of the unbounded derivation which generates the automorphism group.     

Two-photon spectral coherence matrix and characterization of multi-parameter entangled states

In this Letter we discuss how the classical coherence matrix can be generalized to describe the quantum properties of broadband two-photon entangled states. Procedures for experimental evaluation of two-photon matrix elements have been outlined. We illustrate how this formalism can be used for characterization of multi-parameter optical entanglement and discuss its possible applications in quantum optical measurement and quantum coherent control.     

On uniqueness of KMS states of one-dimensional quantum lattice systems

We present a proof of the theorem on the uniqueness of KMS states of one-dimensional quantum lattice systems, which is based on some equicontinuity.     

Resistance inequalities for KMS states of the isotropic Heisenberg model

Inequalities which show that the spin correlations between spins at two lattice sites is bounded by a constant times the inverse square root of the electrical resistance between the lattice sites is proved for KMS states of the isotropic Heisenberg model. The resistance is calculated using the inverse of the coefficients occuring in the Heisenberg Hamiltionian as the resistances between neighboring lattice sites.Work supported in part by a National Science Foundation GrantOn leave from the University of Pennsylvania, Philadelphia, Pa. 19174, USA     

Trace states and KMS states for approximately inner dynamical one-parameter groups of *-automorphisms

The usual definition of approximately inner one-parameter groups of *-automorphisms ofC*-algebras (approximately inner dynamical one-parameter groups) contains a slight asymmetry. When this asymmetry is corrected, we show that if an approximately inner dynamical one-parameter group hasKMS states forone value of inverse temperature =1/kT, then it hasKMS states for all values of . By the Powers-Sakai Theorem it is enough to show that there is a trace state. We obtain a trace state as a limit of a sequence of vector states with respect to a givenKMS state and thus solve a problem raised in [6].Supported by Odense University, Denmark     

A characterization of clustering states

A characterization of states, over quasi-local algebras, which satsfy a strong cluster property is derived. The discussion is applicable to classical systems and quantum systems with Bose or Fermi statistics.     

High‐resolution spectral characterization of two photon states via classical measurements

Quantum optics plays a central role in the study of fundamental concepts in quantum mechanics, and in the development of new technological applications. Typical experiments employ sources of photon pairs generated by parametric processes such as spontaneous parametric down‐conversion and spontaneous four‐wave‐mixing. The standard characterization of these sources relies on detecting the pairs themselves and thus requires single photon detectors, which limit both measurement speed and accuracy. Here it is shown that the two‐photon quantum state that would be generated by parametric fluorescence can be characterised with unprecedented spectral resolution by performing a classical experiment. This streamlined technique gives access to hitherto unexplored features of two‐photon states and has the potential to speed up design and testing of massively parallel integrated nonlinear sources by providing a fast and reliable quality control procedure. Additionally, it allows for the engineering of quantum light states at a significantly higher level of spectral detail, powering future quantum optical applications based on time‐energy photon correlations.     

On the equivalence of KMS and Gibbs conditions for states of quantum lattice systems

The equivalence of a Gibbsian equilibrium condition and the KMS condition is proven for one-dimensional quantum lattice systems with a finite range interaction at arbitrary temperature, and for quantum lattice systems of arbitrary dimension, with a finite body interaction, at high temperature.     

Coherent photon states and spectral condition

A criterion is derived for the existence of a selfadjoint and semibounded momentum operator in a non-Fock representation of the free photon field given by a coherent state. The representation of the translation group is constructed and it is shown that the rotation group, hence the homogeneous Lorentz group, cannot be unitarily implemented in the so-called infrared sectors.     

Prequantization and KMS structures

The properties of the representations of the canonical commutation relations, obtained in the prequantization program, are investigated with special attention to the relevance of the KMS structures in this context. In particular, we show how these structures provide a natural way to pass from the prequantization representation of the CCR to the Schrödinger representation.     

A characterization of Gibbs states of lattice boson systems

We consider lattice boson systems interacting via potentials which are superstable and regular. By using the Wiener integral formalism and the concept of conditional reduced density matrices we are able to give a characterization of Gibbs (equilibrium) states. It turns out that the space of Gibbs states is nonempty, convex, and also weak-compact if the interactions are of finite range. We give a brief discussion on the uniqueness of Gibbs states and the existence of phase transitions in our formalism.     

A Remark on Formal KMS States in Deformation Quantization

Within the framework of deformation quantization, we define formal KMS states on the deformed algebra of power series of functions with compact support in phase space as C[[]]-linear functionals obeying a formal variant of the usual KMS condition known in the theory of C^*-algebras. We show that for each temperature KMS states always exist and are up to a normalization equal to the trace of the argument multiplied by a formal analogue of the usual Boltzmann factor, a certain formal star exponential.     

Core states and spectral flow in vortex dynamics

I review the semi-classical picture of how states bound in the core of a vortex in an S-wave superconductor respond to relative motion between the vortex and the condensate. I show how the momentum absorbed as a result of the Magnus force acting on the core leads to a change in the distribution of occupied states (“spectral flow”). In the simplest relaxation time approximation this modified distribution gives rise to the Kopnin–Kravtsov force on the vortex.     

KMS States and Conformal Measures

From a non-constant holomorphic map on a connected Riemann surface we construct an étale second countable locally compact Hausdorff groupoid whose associated groupoid C*-algebra admits a one-parameter group of automorphisms with the property that its KMS states correspond to conformal measures in the sense of Sullivan. In this way certain quadratic polynomials give rise to quantum statistical models with a phase transition arising from spontaneous symmetry breaking.