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.     

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.     

Passive states for finite classical systems

Starting from a passivity condition based on the second law of thermodynamics [12], we show that ground states and Gibbs states (0<<) are essentially the only passive states.Research supported by M. Skodowska-Curie Fund Grant No. OIP74-01416.     

The Onsager relations for quantum systems weakly coupled to KMS reservoirs

We show that the Onsager relations for energy and matter flows through small quantum systems are generically direct consequences of the KMS (Kubo-Martin-Schwinger) property of the reservoir (Gibbs) equilibrium states in the (van Hove) weak coupling limit.     

KMS conditions and local thermodynamical stability of quantum lattice systems

We formulate local thermodynamical stability conditions for states of quantum lattice systems, and show that these conditions are implied by, and in the case of translationally invariant states equivalent to, those of Kubo-Martin-Schwinger (KMS).     

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.     

Local transformations and KMS states

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

Direct measurement for general quantum states using parametric quantum circuits

In the field of quantum information,the acquisition of information for unknown quantum states is very important.When we only need to obtain specific elements of a state density matrix,the traditional quantum state tomography will become very complicated,because it requires a global quantum state reconstruction.Direct measurement of the quantum state allows us to obtain arbitrary specific matrix elements of the quantum state without state reconstruction,so direct measurement schemes have obtained...     

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.     

KMS conditions and local thermodynamical stability of quantum lattice systems. II

We prove that local thermodynamical stability (LTS), as defined in [1], implies the KMS conditions in quantum lattice systems, without any assumption of translational invariance. This result, together with those of [1], establishes the equivalence between the LTS and the KMS conditions for such systems.     

Optimal measurements for general quantum systems

We give a general formulation of the theory of optimal quantum measurements, based on Gudder's [8] convex structure approaches to axiomatic quantum mechanics, which includes the case of Holevo's formulation [14] and operational quantum mechanics [3]. Simple and general conditions for existence of Bayes optimal measurements are obtained by a method without operator valued measure techniques. For this purpose, a representation of convex prestructures and a characterization of a class of loss functions are obtained. Finally, an application of the results to Wald's theory of statistical decision functions is shown.     

Quasidistributions and coherent states for finite-dimensional quantum systems

In recent years, an approach to discrete quantum phase spaces which comprehends all the main quasiprobability distributions known has been developed. It is the research that started with the pioneering work of Galetti and Piza, where the idea of operator bases constructed of discrete Fourier transforms of unitary displacement operators was first introduced. Subsequently, the discrete coherent states were introduced, and finally, the s-parametrized distributions, that include the Wigner, Husimi, and Glauber–Sudarshan distribution functions as particular cases. In the present work, we adapt its formulation to encompass some additional discrete symmetries, achieving an elegant yet physically sound formalism.     

Scale-renormalized matrix-product states for correlated quantum systems

A generalization of matrix product states (MPS) for interacting quantum systems in two and three dimensions is introduced. These scale-renormalized matrix-product states (SR-MPS) are based on a coarse graining of the lattice in which the blocks at each level are associated with matrix products that are further transformed (scale renormalized) with other matrices before they are assembled to form blocks at the next level. Using the two-dimensional transverse-field Ising model as a test, it is shown that the SR-MPS converge much more rapidly with the matrix size than a standard MPS. It is also shown that the use of lattice symmetries speeds up the convergence very significantly.     

Geometric phase for adiabatic evolutions of general quantum states

The concept of a geometric phase (Berry's phase) is generalized to the case of noneigenstates, which is applicable to both linear and nonlinear quantum systems. This is particularly important to nonlinear quantum systems, where, due to the lack of the superposition principle, the adiabatic evolution of a general state cannot be described in terms of eigenstates. For linear quantum systems, our new geometric phase reduces to a statistical average of Berry's phases. Our results are demonstrated with a nonlinear two-level model.     

A spectral characterization of KMS states

Let be a state on aC*-dynamical system . For each of the following properties of : (1) is -K MS with respect to for some given , 0<+, (2) is either a KMS state or a ground state, necessary and sufficient conditions are given involving only the spectral subspaces of associated with . The results provide a new insight in the concept of passivity, introduced by W. Pusz and S. L. Woronowicz.Aangesteld navorser N.F.W.O., Belgium, on leave from Katholieke Universiteit Leuven. Research partially supported by N.A.T.O.     

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.     

Quantum states and potentialities of quantum systems

In a previous article it was shown that in general quantum states represent perspectives on the potentialities of quantum systems, rather than the potentialities themselves. In the present paper the following questions are investigated in the context of this result: (1) How do quantum states which undergo collapse transform under pure translations? (2) Under what conditions do quantum states represent the potentialities themselves? Two alternatives are presented in response to the first question: (1) Quantum states are scalars under translations. (2) The collapse of a quantum state propagates between frames of reference at the speed of light. The advantages and disadvantages of the two alternatives are discussed. The response to the second question is shown to depend on the chosen alternative. In addition, the second alternative is shown to lead to a consistent view of quantum states as “potential perspectives on potentialities.”     

Ground states of quantum spin systems

We prove that ground states of quantum spin systems are characterized by a principle of minimum local energy and that translationally invariant ground states are characterized by the principle of minimum energy per unit volume.