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1.
We discuss the possibility of automatic simplification of formulas in orthomodular lattices. We describe the principles of
a program which decides the validity of equalities and inequalities, as well as implications between them and other important
relations significant in quantum mechanics.
PACS: 02.10.-v, 02.10.Ab, 02.10.De, 03.65.Fd.
AMS Subject classification: 06C15, 03G12, 06B10, 06B25, 81P10. 相似文献
3.
René Mayet 《International Journal of Theoretical Physics》2006,45(7):1216-1246
We produce and study several sequences of equations, in the language of orthomodular lattices, which hold in the ortholattice of closed subspaces of any classical Hilbert space, but not in all orthomodular lattices. Most of these equations hold in any orthomodular lattice admitting a strong set of states whose values are in a real Hilbert space. For some of these equations, we give conditions under which they hold in the ortholattice of closed subspaces of a generalised Hilbert space. These conditions are relative to the dimension of the Hilbert space and to the characteristic of its division ring of scalars. In some cases, we show that these equations cannot be deduced from the already known equations, and we study their mutual independence. To conclude, we suggest a new method for obtaining such equations, using the tensorial product.
PACS numbers: 02.10, 03.65, 03.67 相似文献
4.
Peng-ming Zhang Xi-guo Lee Shao-feng Wu Yi-shi Duan 《International Journal of Theoretical Physics》2007,46(7):1753-1762
We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations
is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are
determined by the φmapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be
described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations.
PACS 02.10.Kn, 02.40.-k, 11.15.-q 相似文献
5.
Various conditions ensuring that an atomic effect algebra is a Boolean algebra are presented.
PACS: 02.10.-v. 相似文献
6.
A test space is a collection of non-empty sets, usually construed as the catalogue of (discrete) outcome sets associated with a family
of experiments. Subject to a simple combinatorial condition called algebraicity, a test space gives rise to a “quantum logic”—that is, an orthoalgebra. Conversely, all orthoalgebras arise naturally from
algebraic test spaces. In non-relativistic quantum mechanics, the relevant test space is the set ℱ F(H) of frames (unordered orthonormal bases) of a Hilbert space H. The corresponding logic is the usual one, i.e., the projection lattice L(H) of H. The test space ℱ F(H) has a strong symmetry property with respect to the unitary group of H, namely, that any bijection between two frames lifts to a unitary operator. In this paper, we consider test spaces enjoying
the same symmetry property relative to an action by a compact topological group. We show that such a test space, if algebraic,
gives rise to a compact, atomistic topological orthoalgebra. We also present a construction that generates such a test space
from purely group-theoretic data, and obtain a simple criterion for this test space to be algebraic.
PACS: 02.10.Ab; 02.20.Bb; 03.65.Ta. 相似文献
7.
We prove that the algebra of effects in the phase space formalism of quantum mechanics forms an M. V. effect algebra and moreover
a Heyting effect algebra. It contains no nontrivial projections. We equip this algebra with certain nontrivial projections
by passing to the limit of the quantum expectation with respect to any density operator.
PACS: Primary 02.10.Gd, 03.65.Bz, Secondary 002.20.Qs
This paper was a submission to the Sixth International Quantum Structure Association Conference (QS6), which took place in
Vienna, Austria, July 1–7, 2002. 相似文献
8.
The aim of this survey paper is to summarize the most recent results on pre-Hilbert-space logics and their corresponding measure
spaces.
PACS: 02.10.
The paper is dedicated to the memory of Prof. Günter Bruns. 相似文献
9.
D. Bar 《International Journal of Theoretical Physics》2006,45(4):765-789
We have previously discussed the classical diffusive system of the bounded one-dimensional multitrap using the transfer matrix method which is generally applied for studying the energy spectrum of the unbounded quantum Kronig–Penney multibarrier. It was shown, by this method, that for certain values of the relevant parameters the bounded multitrap array have unity transmission and a double-peak phase transitional behavior. We discuss in this work, using the same transfer matrix method, the energy related to the diffusion through the unbounded one-dimensional multitrap and find that it may be expressed in two entirely different ways with different results and consequences. Also, it is shown that, unlike the barriers in the Kronig–Penney case, the energies at one face of the imperfect trap greatly differ from the energies at the other face of the same trap.
PACS: 71.15.Ap, 66.30.-h, 02.10.Yn 相似文献
10.
We present two equivalent axiomatizations for a logic of quantum actions: one in terms of quantum transition systems, and the other in terms of quantum dynamic algebras. The main contribution of the paper is conceptual, offering a new view of quantum structures in terms of their underlying
logical dynamics. We also prove Representation Theorems, showing these axiomatizations to be complete with respect to the natural Hilbert-space semantics. The advantages of this setting are many: (1) it provides a clear and intuitive dynamic-operational meaning to key postulates
(e.g. Orthomodularity, Covering Law); (2) it reduces the complexity of the Solèr–Mayet axiomatization by replacing some of
their key higher-order concepts (e.g. “automorphisms of the ortholattice”) by first-order objects (“actions”) in our structure;
(3) it provides a link between traditional quantum logic and the needs of quantum computation.
PACS: 02.10.-v Logic; set theory and algebra; 03.65.-w Quantum mechanics; 03.65.Fd Algebraic methods; 03.67.-a Quantum information. 相似文献
11.
A. P. Zhernov 《Journal of Experimental and Theoretical Physics》1998,87(2):357-364
Features of the thermal expansion coefficient α(T) of crystal lattices with different isotopic compositions have been analyzed. The case of germanium lattices has been studied
in detail.
Zh. éksp. Teor. Fiz. 114, 654–668 (August 1998) 相似文献
12.
The rules of union and intersection of probabilistic fuzzy sets guided us to construct a related operator algebra. In a Hilbert space, where each fuzzy set is represented by an orthonormal vector, the union and the intersection operators generate a well-defined algebra with a unique representation.
PACS NUMBER: 02.10.-v 相似文献
13.
We begin with a quantum logic carrying a large collection of states. We then form a dual pair of Banach spaces—base normed
and order unit normed—containing the states and the logic, respectively. A Galois connection on the face lattices of the states
and the dual positive order unit interval is introduced. The elements of the logic are connected to a dense subset of the
extreme points of this order interval in the order unit space using a generalized form of the Hahn–Jordan decomposition theorem.
Decision effects are defined and identified with the elements of the original logic. Finally, an important axiom of Ludwig
is introduced which ties together all the lattices of Galois closed faces of states, Galois closed order intervals of the
positive order unit interval, decision effects, and the original quantum logic. The emphasis here is on the consequences of
functional analytic assumptions. The paper concludes with a simple example where Ludwig’s axiom does not hold and we see parts
of the theory dissolve.
PACS: 02.30.Sa, 03.65.Ta. 相似文献
14.
A numerical measure of the difference between crystal lattices is determined. The fruitfulness of the definition is demonstrated
for a specific example concerning the prominence of an orientational correspondence between the body-centered crystal lattice
[bcc(bct)] of α-martensite and the face-centered crystal lattice (fcc) of γ-austenite in cases where the latter is perfect and where it differs from a perfect lattice near a screw dislocation.
Zh. Tekh. Fiz. 69, 60–64 (May 1999) 相似文献
15.
Daniel Lehmann Kurt Engesser Dov M. Gabbay 《International Journal of Theoretical Physics》2006,45(4):698-723
In quantum physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties of such operators are justified on epistemological grounds. Commutation of measurements is a central topic of interest. Classical logical systems may be viewed as measurement algebras in which all measurements commute.
PACS: 02.10.-V. 相似文献
16.
Defining an addition of the effects in the formalism of quantum mechanics on phase space, we obtain a new effect algebra that
is strictly contained in the effect algebra of all effects. A new property of the phase space formalism comes to light, namely
that the new effect algebra does not contain any pair of noncommuting projections. In fact, in this formalism, there are no
nontrivial projections at all. We illustrate this with the spin-1/2 algebra and the momentum/position algebra. Next, we equip
this algebra of effects with the sequential product and get an interpretation of why certain properties fail to hold.
PACS: 02.10.Gd, 03.65.Bz.
This paper was a submission to the Fifth International Quantum Structure Association Conference (QS5), which took place in
Cesena, Italy, March 31–April 5, 2001. 相似文献
17.
Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems
with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in nuclear and
hadronic dynamics. They differ from traditional Bohr–Mottelson models where SL(n,ℝ) is used as a so-called non-invariance group. There is an interesting relationship between classical and quantized integrable
lattices.
PACS: 11.30.Ly, 02.20.-a, 21.60.Ev. 相似文献
18.
It is shown that axially symmetric two-dimensional nonuniform states can exist in easy-axis and cubic antiferromagnets lacking
inversion symmetry, in the form of two-dimensional spatially modulated structures (magnetic vortex lattices) and isolated
two-dimensional structures (vortices). The structure and equilibrium dimensions of the lattices and vortices have been determined
by numerical solution of differential equations.
Fiz. Tverd. Tela (St. Petersburg) 40, 1486–1493 (August 1998) 相似文献
19.
We examine theoretically the generation of electromagnetic radiation in the relative motion of vortex lattices in magnetically
coupled films in the dc transformer geometry. We establish the conditions under which the force of mutual pinning of the vortex
lattices varies according to a harmonic law as a function of the relative displacement of the vortices in the films within
a given range of magnetic field inductions. In this case the equation describing the viscous flow of vortex lattices in magnetically
coupled films is the same as the equation of the resistively shunted Josephson junction model. We show that magnetically coupled
superconductors exhibit the properties of a Josephson element without any restrictions on the geometrical size of such a system
imposed by the coherence length ξ. The frequency f of the electromagnetic radiation generated by the relative motion of vortex lattices in magnetically coupled superconductors
depends on the spatial period of the vortex lattices and the velocity of relative vortex motion, which means that the frequency
of the radiation can be tuned by applying a magnetic field or a current.
Zh. éksp. Teor. Fiz. 113, 1319–1338 (April 1998) 相似文献
20.
A. P. Zhernov 《Physics of the Solid State》1998,40(10):1658-1660
The linear thermal expansion coefficient of crystal lattices of germanium with different isotopic compositions is analyzed.
Fiz. Tverd. Tela (St. Petersburg) 40, 1829–1831 (October 1998) 相似文献