Variational derivation of mean field theories with mixed states

J.Da. Providência, Carlos Fiolhais

A. Kuriyama, João da Providência, Y. Tsue +1 more

In order to compare the approach of the mixed state representation of the pairing model with the exact evaluation of the grand partition function, we introduce the fermion space of a grand canonical ensemble. For the definition of the grand partition function, we adopt a quasi-spin space and evaluate its multiplicity. then we show how to derive the mixed state representation, which yields results that are approximately the same as those of the thermal Hartree-Fock-Bogoliubov theory for the thermal equilibrium state, from the grand partition function under the mean field approximation. We compare numerical results of the mean field approximation with those obtained from the exact evaluation of the grand partition function. We find that the mean field approximation gives good results. However, we find a distinctive difference between the two sets of results in the condensed phase.

Yoshio Kuramoto

M. Yamamura, A. Kuriyama, Y. Tsue

To appear in those proceedings.OCR Output 'Invited talk presented by M. Y. at the conference on "Many-Body Physics", Coimbra, Portugal, mixed states in highly excited nucleus.5•°•7 been formulated as the Dirac canonical formalism with constraints in order to describe the time-dependent variational principle and thermo field dynamics.This theory has Fiolhais, have also developed a microscopic theory for mixed states based on both is investigated.4Two of the authors (M.Y. and A.K.), together with Providéncia and based on the thermo field dynamics and the variation of the thermodynamic potential the thermo field dynamicsz has progressed,3 and the relation between the treatments description of mixed states in many-fermion systems.}Also, the treatment based on For example, the thermal boson expansion theory has been studied in the microscopic various attempts to describe the systems in the excited states have been developed.particle physics.In the field of microscopic theory in nuclear many-body systems, in highly excited states, has been one of the interesting problems in quantum many-The theoretical study of systems in highly excited states, such as nucleus observed a correct classical counterpart is examined and explicitly constructed as "mixed-means of time-dependent variational procedure, a possible state which can offerIn order to investigate quantal systems governed by su(1,1)-algebra by

Jérôme Rosanvallon

Understand the intrinsic physical meaning of quantum formalism leads ontologically to admit that one fundamental side of reality is purely contradictory, irreducibly random, objectively indeterminate and intrinsically independent of relativistic space-time. It means also that physical reality has another fundamental side, i.e. space-time, and that both are irreducible to each other. Quantum reality, discretized by the Planck constant, assume coherent states and partially ordered variables (that are commutative or not), while on the other side, relativistic space-time, structured by the speed of light, assume coherent variables and partially ordered states (that are causally related or not). From this point of view, fields would be only a derived mixture of these two sides. But quantum reality and relativistic space-time seem to be mixed in two kinds of fields themselves irreducible to each other. If, on one hand, quantum field theory has already formalized the way that quantum reality locates, evolves and interacts on a relativistic background, on the other hand, quantum gravity tends to formalize the way that smooth and causally ordered space-time emerges on a quantum background. But no unification of the two fundamental sides of reality must be waited at this derived level. Unification could perhaps intervene only upstream, in a pure variation preceding and underlying its double distinction in variables and states of variation, i.e. its quantization or its localization and their derived mixtures.

Dieter Vollhardt, Krzysztof Byczuk, Marcus Kollar