scholarly journals SNEG – Mathematica package for symbolic calculations with second-quantization-operator expressions

2011 ◽  
Vol 182 (10) ◽  
pp. 2259-2264 ◽  
Author(s):  
Rok Žitko
Keyword(s):  
Second Quantization ◽  
Symbolic Calculations ◽  
Quantization Operator

scholarly journals Invariant nuclear space of a second quantization operator

1995 ◽  
Vol 25 (3) ◽  
pp. 541-559
Author(s):  
Hong Chul Chae ◽  
Kenji Handa ◽  
Itaru Mitoma ◽  
Yoshiaki Okazaki
Keyword(s):  
Nuclear Space ◽  
Second Quantization ◽  
Quantization Operator

scholarly journals Hölder-Type Inequalities for Norms of Wick Products

2008 ◽  
Vol 2008 ◽  
pp. 1-22 ◽  
Author(s):  
Alberto Lanconelli ◽  
Aurel I. Stan
Keyword(s):  
Random Variable ◽  
Upper Bounds ◽  
Minimal Condition ◽  
Wick Product ◽  
Identity Operator ◽  
Second Quantization ◽  
Measurable Functions ◽  
Quantization Operator ◽  
Wick Products ◽  
Finite Moments

Various upper bounds for the L2-norm of the Wick product of two measurable functions of a random variable X, having finite moments of any order, together with a universal minimal condition, are proven. The inequalities involve the second quantization operator of a constant times the identity operator. Some conditions ensuring that the constants involved in the second quantization operators are optimal, and interesting examples satisfying these conditions are also included.

BAYES' FORMULA FOR SECOND QUANTIZATION OPERATORS

2006 ◽  
Vol 06 (02) ◽  
pp. 245-253 ◽  
Author(s):  
ALBERTO LANCONELLI
Keyword(s):  
Conditional Expectation ◽  
Bayes Rule ◽  
Second Quantization ◽  
Absolutely Continuous ◽  
Bayes Formula ◽  
Conditional Expectations ◽  
Quantization Operator ◽  
Continuous Measures ◽  
The Relationship ◽  
Absolutely Continuous Measures

The Bayes' formula provides the relationship between conditional expectations with respect to absolutely continuous measures. The conditional expectation is in the context of the Wiener space — an example of second quantization operator. In this note we obtain a formula that generalizes the above-mentioned Bayes' rule to general second quantization operators.

Generalization of the New Resonance Theory: Second Quantization Operator, Localization Scheme, and Basis Set

2009 ◽  
Vol 5 (7) ◽  
pp. 1741-1748 ◽  
Author(s):  
Atsushi Ikeda ◽  
Yoshihide Nakao ◽  
Hirofumi Sato ◽  
Shigeyoshi Sakaki
Keyword(s):  
Basis Set ◽  
Second Quantization ◽  
Resonance Theory ◽  
Localization Scheme ◽  
Quantization Operator

A HÖLDER INEQUALITY FOR NORMS OF POISSONIAN WICK PRODUCTS

2013 ◽  
Vol 16 (03) ◽  
pp. 1350022 ◽  
Author(s):  
ALBERTO LANCONELLI ◽  
AUREL I. STAN
Keyword(s):  
Hölder Inequality ◽  
Wick Product ◽  
Identity Operator ◽  
Second Quantization ◽  
Charlier Polynomials ◽  
Quantization Operator ◽  
Wick Products

An understanding of the second quantization operator of a constant times the identity operator and the Poissonian Wick product, without using the orthogonal Charlier polynomials, is presented first. We use both understanding, with and without the Charlier polynomials, to prove some inequalities about the norms of Poissonian Wick products. These inequalities are the best ones in the case of L1, L2, and L∞ norms. We close the paper with some probabilistic interpretations of the Poissonian Wick product.

ON HEISENBERG INEQUALITY

2005 ◽  
Vol 07 (01) ◽  
pp. 75-88
Author(s):  
AUREL STAN
Keyword(s):  
White Noise ◽  
Unitary Operator ◽  
Noise Analysis ◽  
Differentiation Operator ◽  
White Noise Analysis ◽  
Second Quantization ◽  
Quantization Operator ◽  
Heisenberg Inequality

A Heisenberg inequality, involving a differentiation operator, its adjoint, and the second quantization operator of a unitary operator, is proved in the context of white noise analysis.

The limit state of concrete and reinforced concrete rods at complex and longitudinal-transverse bending

2020 ◽  
pp. 60-73
Author(s):  
Yu V Nemirovskii ◽  
S V Tikhonov
Keyword(s):  
General Solution ◽  
Least Squares ◽  
Nonlinear Differential Equations ◽  
Limit State ◽  
Algebraic Equations ◽  
Method Of Least Squares ◽  
Elasticity Limit ◽  
Limit Values ◽  
Symbolic Calculations ◽  
Deformation Diagrams

The work considers rods with a constant cross-section. The deformation law of each layer of the rod is adopted as an approximation by a polynomial of the second order. The method of determining the coefficients of the indicated polynomial and the limit deformations under compression and tension of the material of each layer is described with the presence of three traditional characteristics: modulus of elasticity, limit stresses at compression and tension. On the basis of deformation diagrams of the concrete grades B10, B30, B50 under tension and compression, these coefficients are determined by the method of least squares. The deformation diagrams of these concrete grades are compared on the basis of the approximations obtained by the limit values and the method of least squares, and it is found that these diagrams approximate quite well the real deformation diagrams at deformations close to the limit. The main problem in this work is to determine if the rod is able withstand the applied loads, before intensive cracking processes in concrete. So as a criterion of the conditional limit state this work adopts the maximum permissible deformation value under tension or compression corresponding to the points of transition to a falling branch on the deformation diagram level in one or more layers of the rod. The Kirchhoff-Lyav classical kinematic hypotheses are assumed to be valid for the rod deformation. The cases of statically determinable and statically indeterminable problems of bend of the rod are considered. It is shown that in the case of statically determinable loadings, the general solution of the problem comes to solving a system of three nonlinear algebraic equations which roots can be obtained with the necessary accuracy using the well-developed methods of computational mathematics. The general solution of the problem for statically indeterminable problems is reduced to obtaining a solution to a system of three nonlinear differential equations for three functions - deformation and curvatures. The Bubnov-Galerkin method is used to approximate the solution of this equation on the segment along the length of the rod, and specific examples of its application to the Maple system of symbolic calculations are considered.

Identical Particles and Second Quantization: Occupation Number Representation

2018 ◽  
Author(s):  
Norman J. Morgenstern Horing
Keyword(s):  
Occupation Number ◽  
Annihilation Operator ◽  
Pauli Exclusion Principle ◽  
Exclusion Principle ◽  
Number Representation ◽  
Second Quantization ◽  
Identical Particles ◽  
Fundamental Properties ◽  
Minimum Uncertainty ◽  
Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

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