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1.
We consider a representation of the entropy production for a completely positive, trace-preserving dynamical semigroup satisfying detailed balance with respect to its faithful stationary state denned on aW*-algebra(): it is expressed as a positive Hermitian form on(), which is analogous to the quantum correlation functions used in the Kubo theory. By considering this Hermitian form as a variation function of a vector in(), an exact characterization of the stationary states of semigroups in a certain class is obtained. On this basis, the problem of characterizing the stationary states discussed by Spohn and Lebowitz for manyreservoir open systems is solved without the restriction to situations near thermal equilibrium.  相似文献   

2.
We give an algebraic condition in order that a completely positive dynamical semigroup of an N-level system has a unique (invariant) equilibrium state and that every initial state approaches this equilibrium state as t . We apply our result to a semigroup arising in the weak coupling limit.  相似文献   

3.
A concise geometrodynamic approach to quantum theory is introduced, via a quo;quantum connectionQ µ , which is the affine connection in Hilbert space. It is emphasized that this is the simplest and most natural interpretation of quantum mechanics in general relativity and yet has been largely neglected, so that much work remains to be done on it. The generalized Hilbert space has a simple Hermitian metric, but the precise form ofQ µ remains to be determined. The quantum connection is matheamtically analogous to the spinor connection, which is discussed here for that reason, although the spinor connection arises in the first quantization, whereasQ µ geometrizes the second quantization.  相似文献   

4.
Aquantum logic (-orthocomplete orthomodular poset L with a convex, unital, and separating set of states) is said to have theexistence property if the expectation functionals onlin() associated with the bounded observables of L form a vector space. Classical quantum logics as well as the Hilbert space logics of traditional quantum mechanics have this property. We show that, if a quantum logic satisfies certain conditions in addition to having property E, then the number of its blocks (maximal classical subsystems) must either be one (classical logics) or uncountable (as in Hilbert space logics).Part of this work was done while the author was a visitor at the Department of Mathematics and Computer Science of the University of Denver, Denver, Colorado.  相似文献   

5.
Thes2 quantized Knizhnik-Zamolodchikov equations are solved inq-hypergeometric functions. New difference equations are derived for generalq-hypergeometric functions. The equations are given in terms of quantum Yang-Baxter matrices and have the form similar to quantum Knizhnik-Zamolodchikov equations for quantum affine algebras introduced by Frenkel and Reshetikhin.This work was supported by NSF grant DMS-9203929.  相似文献   

6.
The ground state and first few excited energy levels of the generalized anharmonic oscillator defined by the HamiltonianH=–d 2/dx 2+x 2+x 2k (k=3, 4,...) have been calculated by employing the method of quantum normal form, which is the quantum mechanical analogue of the classical Birkhoff-Gustavson normal form. The present energy eigenvalues are consistent with other tabulations of the energy levels.  相似文献   

7.
Homeomorphisms of the unit-sphere of states are studied. Generalizations of the Piron statement and Wigners' theorem are obtained. It is shown that if the semigroup of the unitary operations of quantum theory were extended by introducing any non-linear operation, amobility phenomenon would occur consisting of a possibility of moving any two states to any two surroundings on the unit sphere. For the resulting non-linear wave packets the complementarity doctrine would become impossible because of fluidity of the space of states under the dynamical transformations.Supported by COSNET/SEPOn leave of absence from Institute of Physics, Warsaw University, Warsaw, Poland  相似文献   

8.
The unitary operations which can be generated on many particle states in non-relativistic quantum mechanics are discussed. These operations depend on an arbitrary external field which is in the experimenter's control, whereas the pairwise potential of interaction between the particles is fixed. The various kinds of systems ofN identical particles interacting via the potentials are studied. For every system in question, the semigroup spanned by evolution transformations is proved to contain all the unitary operators in the Hilbert space of states. In particular, it is shown that the natural evolution operation can be reversed by a certain prescribed sequence of maneouvres involving only external fields.  相似文献   

9.
It is shown that the braid generator is diagonalizable on arbitrary tensor product modules V V, V an irreducible module for a quantum group. A generalization of the Reshetikhin form for the braid generator is thereby obtained in the general case. As an application, a general closed formula is determined for link polynomials.  相似文献   

10.
Through a Daniell-Kolmogorov type construction, to any Markov quantum semigroup on aC*-algebra there is associated a quantum stochastic process which is a dilation of the semigroup, and satisfies a covariance rule which implies the weak Markov property.  相似文献   

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