共查询到20条相似文献,搜索用时 0 毫秒
1.
D. A. Slavnov 《Theoretical and Mathematical Physics》2006,149(3):1690-1701
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical
subsystems. This allows using the formal classical logic and classical probability theory in quantum mechanics. Our approach
nevertheless allows completely reproducing the standard mathematical formalism of quantum mechanics and identifying its applicability
limits. We especially attend to the quantum state reduction problem.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 457–472, December, 2006. 相似文献
2.
D. A. Slavnov 《Theoretical and Mathematical Physics》2005,142(3):431-446
We describe a system of axioms that, on one hand, is sufficient for constructing the standard mathematical formalism of quantum mechanics and, on the other hand, is necessary from the phenomenological standpoint. In the proposed scheme, the Hilbert space and linear operators are only secondary structures of the theory, while the primary structures are the elements of a noncommutative algebra (observables) and the functionals on this algebra, associated with the results of a single observation.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 3, pp. 510–529, March, 2005 相似文献
3.
A. Anikin 《Regular and Chaotic Dynamics》2008,13(5):377-402
According to classical result of Moser [1] a real-analytic Hamiltonian with one and a half degrees of freedom near a hyperbolic
fixed point can be reduced to the normal form by a real-analytic symplectic change of variables. In this paper the result
is extended to the case of the non-commutative algebra of quantum observables.We use an algebraic approach in quantum mechanics
presented in [2] and develop it to the non-autonomous case. We introduce the notion of quantum non-autonomous canonical transformations
and prove that they form a group and preserve the structure of the Heisenberg equation. We give the concept of a non-commutative
normal form and prove that a time-periodic quantum observable with one degree of freedom near a hyperbolic fixed point can
be reduced to a normal form by a canonical transformation. Unlike traditional results, where only formal theory of normal
forms is constructed, we prove a convergence of the normalizing procedure.
相似文献
4.
A. S. Holevo 《Journal of multivariate analysis》1973,3(4):337-394
Quantum statistical decision theory arises in connection with applied problems of optimal detection and processing of quantum signals. In this paper we give a systematic treatment of this theory, based on operator-valued measures. We study the existence problem for optimal measurements and give sufficient and necessary conditions for optimality. The notion of the maximum likelihood measurement is introduced and investigated. The general theory is then applied to the case of Gaussian (quasifree) states of Bose systems, for which optimal measurements of the mean value are found. 相似文献
5.
We continue the classification, begun in [11], [14] and [12], of quadratic Artin-Schelter regular algebras of global dimension 4 which map onto a twisted homogeneous coordinate ring of a quadric hypersurfcice in P3. In this paper, we consider those cases where the quadric has rank 3. We also give sufficient conditions for the point scheme of any quadratic regular algebra of global dimension 4 to be the graph of an automorphism. 相似文献
6.
7.
A. F. Vasil'ev 《Mathematical Notes》1997,62(1):44-49
In 1968 Carter, Fisher, and Hawkes developed the method of extremal classes to study local formations and their critical groups
in the class of finite solvable groups. In the present paper the problem of Shemetkov on the extension of this method to arbitrary
finite groups is solved.
Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 52–58, July, 1997.
Translated by A. I. Shtern 相似文献
8.
9.
10.
11.
K. Keremedis 《Algebra Universalis》1996,36(4):564-572
It is shown that the axiom of choice AC is equivalent to the statements: (1)For every Boolean ring (B, +, ·)and every subset H B which is closed under + there exists a –maximal ideal QB such that H Q={0} and, (2)For every Boolean ring (B,+,·),for every A B, the infinite system:X
i + yi=bi,iI, b
i
B has a solution in A iff each of its equations has a solution in A.Presented by G. Grätzer 相似文献
12.
Bingren Li 《中国科学A辑(英文版)》1998,41(6):574-581
On a Borel bar space (E,B,-), the following concepts are introduced in a suitable way: measurable fields of real Hilbert spaces, real measurable fields
of vectors, operators and Von Neumann (VN) algebras: ξ (⋅),a (⋅),M (⋅). Then a satisfactory real reduction theory is obtained: a real VN algebraM can be represented as a direct integral
where each VN algebraM(t) in this field will be simpler. 相似文献
13.
Shiro Ishikawa 《Fuzzy Sets and Systems》1997,90(3):3809-306
Recently, we proposed a general measurement theory for classical and quantum systems (i.e., “objective fuzzy measurement theory”). In this paper, we propose “subjective fuzzy measurement theory”, which is characterized as the statistical method of the objective fuzzy measurement theory. Our proposal of course has a lot of advantages. For example, we can directly see “membership functions” (= “fuzzy sets”) in this theory. Therefore, we can propose the objective and the subjective methods of membership functions. As one of the consequences, we assert the objective (i.e., individualistic) aspect of Zadeh's theory. Also, as a quantum application, we clarify Heisenberg's uncertainty relation. 相似文献
14.
V.K. Srinivasan 《International Journal of Mathematical Education in Science & Technology》2013,44(3):387-398
The author introduces the birthday problem in this article. This can amuse willing members of any birthday party. This problem can also be used as the motivational first day lecture in number theory for the gifted students in high schools or in community colleges or in undergraduate classes in colleges. 相似文献
15.
16.
A. S. Holevo 《Journal of multivariate analysis》1975,5(4):462-465
A generalization of a vector-valued integral arising in the noncommutative (quantum) statistical decision theory is considered. 相似文献
17.
S. T. Rachev 《Queueing Systems》1989,4(4):287-317
The stability problem in queueing theory is concerned with the continuity of the mappingF from the setU of the input flows into the setV of the output flows. First, using the theory of probability metrics we estimate the modulus ofF-continuity providing thatU andV have structures of metric spaces. Then we evaluate the error terms in the approximation of the input flows by simpler ones assuming that we have observed some functionals of the empirical input flows distributions.Research initiated under support by Army Office of Scientific Research through Mathematical Sciences Institute during the author's visit to MSI in December 1988. References 相似文献
18.
We classify all the indecomposable modules of dimension ≤ 5 over the quantum exterior algebra k(x, y)/(x^2, y^2, xy + qyx) in two variables, and all the indecomposable modules of dimension ≤3 over the quantum complete intersection k(x,y)/(x^m,y^n,xy + qyx) in two variables, where m or n ≥3, by giving explicitly their diagram presentations. 相似文献
19.
Carlos M. Mora 《Journal of Functional Analysis》2008,255(12):3249-3273
This paper deals with open quantum systems. In particular, we focus on the adjoint quantum master equations with initial conditions given by unbounded operators. Examples of this type of initial data are the position and momentum operators of quantum oscillators and the occupation number operator in many-body particle systems. The article establishes the existence and uniqueness of solutions of the operator equations governing the motion of unbounded observables under the Born-Markov approximations. To this end, we develop the relation between operator evolution equations arising in quantum mechanics and stochastic evolutions equations of Schrödinger type. Furthermore, we examine quantum dynamical semigroup properties of the Heisenberg evolutions of general classes of observables. 相似文献
20.
Sergei Abramovich Andrew Brantlinger 《International Journal of Mathematical Education in Science & Technology》2013,44(3):317-333
This paper shows how the computational and graphical capabilities of spreadsheets allow for interactive analytic and geometric constructions from numerical modelling of homogeneous Diophantine equations of the second order. Suggested activities, designed for prospective teachers of mathematics and made possible by what is referred to in the paper as the tool kit approach, enable one to revisit classic mathematics concepts within the framework of computerized mathematical experiment. 相似文献