共查询到20条相似文献,搜索用时 0 毫秒
1.
2.
Using basic ideas from algebraic geometry, we extend the methods of Lagrangian and symplectic mechanics to treat a large class of discrete mechanical systems, that is, systems such as cellular automata in which time proceeds in integer steps and the configuration space is discrete. In particular, we derive an analog of the Euler-Lagrange equation from a variational principle, and prove an analog of Noether's theorem. We also construct a symplectic structure on the analog of the phase space, and prove that it is preserved by time evolution. 相似文献
3.
Within the scope of a new algebraic method for the construction of soliton solutions of nonlinear equations [10–13], concrete examples of the system are considered which are connected with the algebra sl(2, R). 相似文献
4.
Max R. Niedermaier 《Nuclear Physics B》1995,440(3):603-643
An associative *-algebra is introduced (containing a TTR-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each T-invariant linear functional over the algebra automatically satisfies all the form factor axioms. It is argued that this answers the question (posed in the functional Bethe ansatz) how to select the dynamically correct representations of the TTR-algebra. Applied to the case of integrable QFTs with diagonal factorized scattering theory a universal formula for the eigenvalues of the conserved charges emerges. 相似文献
5.
We point out a general relationship between the planar coloring problem withQ colors and the Temperley-Lieb algebra with parameter
. This allows us to give a complete algebraic reformulation of the four color result, and to give algebraic interpretations of various other aspects of planar colorings.Work supported in part by NSF Grant #DMS-882602, the program for Mathematics and Molecular Biology, UC Berkeley, and a visiting fellowship of the Japan Society for the promotion of science at Kyoto University, Kyoto, JapanWork supported in part by DOE Contact #DE-AC02-76ERO3075 and by a Packard Fellowship for Science and Engineering 相似文献
6.
Two different matrix algorithms are described for the restoration of blurred pictures. These are illustrated by numerical examples. 相似文献
7.
We introduce a simple algebraic approach to the study of multipartite entanglement for pure states together with a class of suitable functionals able to detect the entanglement. On this basis, we reproduce some known results. Indeed, by investigating the properties of the introduced functionals, we show that a subset of such class is strictly connected to the purity. Moreover, we provide a direct and basic solution to the problem of simultaneous maximization of three appropriate functionals for three-qubit states, confirming that the simultaneous maximization of the entanglement for all possible bipartitions is compatible only with the structure of the GHZ states. 相似文献
8.
Nirmal Kumar Sarkar Joydeep Choudhury Ramendu Bhattacharjee 《Molecular physics》2013,111(19):3051-3055
Using Lie algebra the vibrational energy levels of HCN were calculated using the local Hamiltonian for 35 vibrational bands. A comparative study was made with earlier results. 相似文献
9.
Herbert Spohn 《Letters in Mathematical Physics》1977,2(1):33-38
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
10.
In this paper we present two algorithms for reducing systems of multivariate polynomial equations over the finite field F 2 to the canonical triangular form called lexicographical Gröbner basis. This triangular form is the most appropriate for finding solutions of the system. On the other hand, the system of polynomials over F 2 whose variables also take values in F 2 (Boolean polynomials) completely describes the unitary matrix generated by a quantum circuit. In particular, the matrix itself can be computed by counting the number of solutions (roots) of the associated polynomial system. Thereby, efficient construction of the lexicographical Gröbner bases over F 2 associated with quantum circuits gives a method for computing their circuit matrices that is alternative to the direct numerical method based on linear algebra. We compare our implementation of both algorithms with some other software packages available for computing Gröbner bases over F 2. 相似文献
11.
Feza Gürsey 《Foundations of Physics》1983,13(3):289-296
The power of the Dirac algebra is illustrated through the Kähler correspondence between a pair of Dirac spinors and a 16-component bosonic field. The SO(5, 1) group acts on both the fermion and boson fields, leading to a supersymmetric equation of the Dirac type involving all these fields. 相似文献
12.
S.G. Rajeev 《Annals of Physics》2010,325(4):899-908
The Kondo problem is approached using the unitary Lie algebra of spin-singlet fermion bilinears. In the limit when the number of values of the spin N goes to infinity the theory approaches a classical limit, which still requires a renormalization. We determine the ground state of this renormalized theory. Then we construct a quantum theory around this classical limit, which amounts to recovering the case of finite N. 相似文献
13.
14.
15.
提出了利用Bernstein多项式对混沌时间序列的动力学方程进行建模的方法,并将该方法与递推最小二乘(RLS)算法相结合,从而可以自适应地逼近混沌时间序列的动力学特性,以达到预测的目的.理论分析和仿真实验表明该方法对一些常见的混沌时间序列具有较高的预测精度和较理想的准确预测率.由于RLS算法的收敛速度较快,因此该方法比较适合于对短混沌时间序列进行实时预测.
关键词:
混沌
预测
Bernstein多项式
RLS算法 相似文献
16.
Srinivasa Rao Karumuri Joydeep Choudhury Nirmal Kumar Sarkar Ramendu Bhattacharjee 《Pramana》2009,72(3):517-525
One of the most interesting areas of current research in molecular physics is the study of the vibrationally excitated states
of medium and large molecules. In view of the considerable amount of experimental activity in this area, one needs theoretical
models within which to interpret experimental data. Using Lie algebraic method, the vibrational energy levels of nickel metalloporphyrins
like Ni(OEP), Ni porphyrin and Ni(TPP) are calculated for 16 vibrational modes. The algebraic Hamiltonian
, where A
i
, A
ij
and λ
ij
are the algebraic parameters which vary from molecule to molecule and C
i
, C
ij
and M
ij
are algebraic operators. The vibrational energy levels are calculated using algebraic model Hamiltonian and the results are
compared with the experimental values. The results obtained by this model are very accurate.
相似文献
17.
José L. Cereceda 《Foundations of Physics》1995,25(6):925-949
In this paper we present a systematic formulation of some recent results concerning the algebraic demonstration of the two major no-hidden-variables theorems for N spin-1/2 particles. We derive explicitly the GHZ states involved and their associated eigenvalues. These eigenvalues turn out to be undefined for N=, this fact providing a new proof showing that the nonlocality argument breaks down in the limit of a truly infinite number of particles. 相似文献
18.
C. M. Edwards 《Communications in Mathematical Physics》1970,16(3):207-230
Recent work of Davies and Lewis has suggested a mathematical framework in which the notion of repeated measurements on statistical physical systems can be examined. This paper is concerned with an examination of their formulation in the abstract and its application to theC*-algebra model for quantum mechanics. In particular, a study is made of the notion of the restriction of a physical system and a definition, which coincides with the usual definition in theC*-algebra model, is formulated. 相似文献
19.
We discuss questions pertaining to the definition of ‘momentum’, ‘momentum space’, ‘phase space’ and ‘Wigner distributions’;
for finite dimensional quantum systems. For such systems, where traditional concepts of ‘momenta’ established for continuum
situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the
purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is
limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail 相似文献
20.
The modification of the Jacobi polynomial expansion method (MJEM) is proposed on the basis of the application of the truncated moments instead of the full ones. This allows us to reconstruct the local quark helicity distributions with high precision even for the narrow Bjorken x region accessible for measurement, using as an input only the four first moments extracted from the data in the next to leading order QCD. The variational (extrapolation) procedure is also proposed allowing us to reconstruct the distributions outside the accessible Bjorken x region using the distributions obtained with MJEM in the accessible region. The numerical calculations encourage one that the proposed variational (extrapolation) procedure could be applied to estimate the full first (especially important) quark moments. 相似文献