On quasi-free dynamics on the resolvent algebra

The resolvent algebra is a new C*-algebra of the canonical commutation relations of a boson field given by Buchholz-Grundling. We study analytic properties of quasi-free dynamics on the resolvent algebra. Subsequently we consider a supersymmetric quasi-free dynamics on the graded C*-algebra made of a Clifford (fermion) algebra and a resolvent (boson) algebra. We establish an infinitesimal supersymmetry formula upon the GNS Hilbert space for any regular state satisfying some mild requirement which is standard in quantum field theory. We assert that the supersymmetric dynamics is given as a C*-dynamics.Comment: This paper has been withdrawn by the author due to its being based on some unjustified assumptions. Also there are mathematically incorrect arguments that stem from the assumption

On fermion grading symmetry

We consider the univalence superselection rule. One would say perhaps ``There is no indication in nature to invalidate this rule. Fermions do not condensate!'' To explain our motivation, let us recall the correspondence of fermion systems and Pauli systems by the Jordan-Wigner transformation. For a finite lattice, fermion grading symmetry corresponds to the Pauli grading. For an infinite lattice, the Pauli-grading can be spontaneously broken e.g. for the XY-model. What is the status of the fermion grading? Nature tells that fermion grading symmmetry cannot be broken for any physical model. But it seems that its rigorous support is needed.Comment: A revised versio

Markov property and strong additivity of von Neumann entropy for graded quantum systems

It is easy to verify the equivalence of the quantum Markov property and the strong additivity of entropy for graded quantum systems as well. However, the structure of Markov states for graded systems is different from that for tensor product systems. For three-composed graded systems there are U(1)-gauge invariant Markov states whose restriction to the pair of marginal subsystems is non-separable.Comment: 14 pages, to appear J. Math. Phy

Joint Extension of States of Subsystems for a CAR System

The problem of existence and uniqueness of a state of a joint system with given restrictions to subsystems is studied for a Fermion system, where a novel feature is non-commutativity between algebras of subsystems. For an arbitrary (finite or infinite) number of given subsystems, a product state extension is shown to exist if and only if all states of subsystems except at most one are even (with respect to the Fermion number). If the states of all subsystems are pure, then the same condition is shown to be necessary and sufficient for the existence of any joint extension. If the condition holds, the unique product state extension is the only joint extension. For a pair of subsystems, with one of the given subsystem states pure, a necessary and sufficient condition for the existence of a joint extension and the form of all joint extensions (unique for almost all cases) are given. For a pair of subsystems with non-pure subsystem states, some classes of examples of joint extensions are given where non-uniqueness of joint extensions prevails.Comment: A few typos are corrected. 19 pages, no figure. Commun.Math.Phys.237, 105-122 (2003

Validity and failure of some entropy inequalities for CAR systems

Basic properties of von Neumann entropy such as the triangle inequality and what we call MONO-SSA are studied for CAR systems. We show that both inequalities hold for any even state. We construct a certain class of noneven states giving counter examples of those inequalities. It is not always possible to extend a set of prepared states on disjoint regions to some joint state on the whole region for CAR systems. However, for every even state, we have its `symmetric purification' by which the validity of those inequalities is shown. Some (realized) noneven states have peculiar state correlations among subsystems and induce the failure of those inequalities.Comment: 14 pages, latex, to appear in JMP. Some typos are correcte

Specific Heats of Fe-Ni (fcc) Alloys at High Temperature

Specific heats at constant pressure, C_p, of Fe-Ni (fcc) alloys have been measured a temperatures 300～1000 K. For alloys containing more than 50%Ni, the C_p-T curve shows a sharp λ-type peak at ferromagnetic Curie temperature. For the alloys less in concentration of nickel, however, only a dull peak is observed. The C_p-T curve is analyzed using the values of thermal expansion coefficient and of compressibility measured on the same conditions, separating the magnetic contribution from total specific heats