scholarly journals The effective mass problem for the Landau-Pekar equations

2021 ◽  
Author(s):  
Dario Feliciangeli ◽  
Simone Rademacher ◽  
Robert Seiringer
Keyword(s):  
Variational Principle ◽  
Effective Mass ◽  
Initial Velocity ◽  
Energy Functional ◽  
Mass Problem ◽  
Definition Of

Abstract We provide a definition of the effective mass for the classical polaron described by the Landau-Pekar equations. It is based on a novel variational principle, minimizing the energy functional over states with given (initial) velocity. The resulting formula for the polaron's effective mass agrees with the prediction by Landau and Pekar.

scholarly journals Nuclear energy functional with a surface-peaked effective mass: global properties

2011 ◽  
Vol 38 (2) ◽  
pp. 025101 ◽  
Author(s):  
A F Fantina ◽  
J Margueron ◽  
P Donati ◽  
P M Pizzochero
Keyword(s):  
Effective Mass ◽  
Nuclear Energy ◽  
Energy Functional ◽  
Global Properties

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

On the symplectically invariant variational principle and generating functions

1990 ◽  
Vol 431 (1883) ◽  
pp. 403-417 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Variational Principle ◽  
Generating Function ◽  
Generating Functions ◽  
Geometric Approach ◽  
Canonical Transformations ◽  
Weyl Transform ◽  
Analogous Relation ◽  
Definition Of ◽  
Symplectic Invariance

The generating function for canonical transformations derived by Marinov has the important property of symplectic invariance (i. e. under linear canonical transformations). However, a more geometric approach to the rederivation of this function from the variational principle reveals that it is not free from caustic singularities after all. These singularities can be avoided without breaking the symplectic invariance by the definition of a complementary generating function bearing an analogous relation to the Woodward ambiguity function in telecommunications theory as that tying Marinov’s function to the Wigner function and the Weyl transform in quantum mechanics. Marinov’s function is specially apt to describe canonical transformations close to the identity, but breaks down for reflections through a point in phase space, easily described by the new generating function.

Reckoning for Element Characteristics Matrix of Space Timoshenko-Beam Based on Energy Variational Principle

2011 ◽  
Vol 66-68 ◽  
pp. 1356-1361
Author(s):  
Wen Jun Pan ◽  
Zhi Wu Wei
Keyword(s):  
Variational Principle ◽  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Mass Matrix ◽  
Research Work ◽  
Energy Functional ◽  
Displacement Function ◽  
Matrix Stiffness ◽  
Stiffness Matrices

To analyze and calculate the element characteristics matrices of space Timoshenko-beam, research work were carried out on the basis of energy variational principle. Displacement function for the space Timoshenko-beam were put forward, the expressions for element mass matrix, stiffness matrix and load array were deduced by energy functional extremum, and the explicit forms of element mass and stiffness matrices were integrated finally. Results show that the element mass and stiffness matrices computed by this method are consistent with those in related references. It has a good theoretical and practical value in the calculation for characteristics matrices of other elements.

Entropy of a Flow on Non-compact Sets

2012 ◽  
Vol 19 (02) ◽  
pp. 1250015 ◽  
Author(s):  
Jinghua Shen ◽  
Yun Zhao
Keyword(s):  
Variational Principle ◽  
Topological Entropy ◽  
Compact Sets ◽  
Entropy Formula ◽  
The One ◽  
Definition Of

Based on the theory of Carathéodory structure, this paper introduces the topological entropy of a flow on non-compact sets. Moreover, we introduce the definition of measure-theoretic entropy of a flow. It is shown that this entropy is equivalent to the one defined by Sun in [10]. The variational principle between topological entropy and measure-theoretic entropy of a flow is established. We also get the Brin-Katok's entropy formula for a flow.

scholarly journals Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory

2010 ◽  
Vol 21 (2) ◽  
pp. 181-203 ◽  
Author(s):  
APALA MAJUMDAR
Keyword(s):  
Three Dimensional ◽  
Energy Functional ◽  
Order Parameters ◽  
Tensor Order ◽  
Temperature Regimes ◽  
Explicit Bounds ◽  
Scalar Order ◽  
Definition Of ◽  
Gennes Theory ◽  
The Continuum

We study equilibrium liquid crystal configurations in three-dimensional geometries, within the continuum Landau-de Gennes theory. We obtain explicit bounds for the equilibrium scalar order parameters in terms of the temperature and material-dependent constants. We explicitly quantify the temperature regimes where the Landau-de Gennes predictions match and the temperature regimes where the Landau-de Gennes predictions do not match the probabilistic second-moment definition of the Q-tensor order parameter. The regime of agreement may be interpreted as the regime of validity of the Landau-de Gennes theory since the Landau-de Gennes theory predicts large values of the equilibrium scalar order parameters – larger than unity, in the low-temperature regime. We discuss a modified Landau-de Gennes energy functional which yields physically realistic values of the equilibrium scalar order parameters in all temperature regimes.

Infinitely Many Solutions for a Non-homogeneous Differential Inclusion with Lack of Compactness

2019 ◽  
Vol 19 (3) ◽  
pp. 625-637 ◽  
Author(s):  
Bin Ge ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Variational Principle ◽  
Differential Inclusion ◽  
Energy Functional ◽  
Mountain Pass Lemma ◽  
Infinitely Many Solutions ◽  
Locally Lipschitz Functions ◽  
Fountain Theorem ◽  
Inclusion Problems ◽  
Locally Lipschitz ◽  
Symmetric Mountain Pass Lemma

Abstract In this paper, we consider the following class of differential inclusion problems in {\mathbb{R}^{N}} involving the {p(x)} -Laplacian: -\Delta_{p(x)}u+V(x)\lvert u\rvert^{p(x)-2}u\in a(x)\partial F(x,u)\quad\text{% in}\ \mathbb{R}^{N}. We are concerned with a multiplicity property, and our arguments combine the variational principle for locally Lipschitz functions with the properties of the generalized Lebesgue–Sobolev space. Applying the nonsmooth symmetric mountain pass lemma and the fountain theorem, we establish conditions such that the associated energy functional possesses infinitely many critical points, and then we obtain infinitely many solutions.

scholarly journals On the variational principle for the non-linear Schrödinger equation

2019 ◽  
Vol 58 (1) ◽  
pp. 340-351
Author(s):  
Zsuzsanna É. Mihálka ◽  
Ádám Margócsy ◽  
Ágnes Szabados ◽  
Péter R. Surján
Keyword(s):  
Variational Principle ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Functional ◽  
Numerical Calculations ◽  
Eigenvalue Equation ◽  
Expectation Value ◽  
Energy Expectation ◽  
Feynman Theorem ◽  
Energy Expectation Value

AbstractWhile variation of the energy functional yields the Schrödinger equation in the usual, linear case, no such statement can be formulated in the general nonlinear situation when the Hamiltonian depends on its eigenvector. In this latter case, as we illustrate by sample numerical calculations, the points of the energy expectation value hypersurface where the eigenvalue equation is satisfied separate from those where the energy is stationary. We show that the variation of the energy at the eigensolution is determined by a generalized Hellmann–Feynman theorem. Functionals, other than the energy, can, however be constructed, that result the nonlinear Schrödinger equation upon setting their variation zero. The second centralized moment of the Hamiltonian is one example.

SHAPE EFFECT OF SEMIMAGNETIC QUANTUM DOT ON THE BOUND MAGNETIC POLARON

2011 ◽  
Vol 10 (04n05) ◽  
pp. 665-668 ◽  
Author(s):  
A. MERWYN JASPER DE REUBEN ◽  
K. JAYAKUMAR
Keyword(s):  
Magnetic Field ◽  
Variational Principle ◽  
Binding Energy ◽  
Quantum Dot ◽  
Effective Mass ◽  
Shape Effect ◽  
Magnetic Polaron ◽  
Bound Magnetic Polaron ◽  
Mass Approximation ◽  
The Magnetic Field

The effect of geometry, concentration of Mn ion and the magnetic field on the binding energy of a donor and the donor bound magnetic polaronic shift in a finite Cd 1–x1 Mn x1 Te / Cd 1–x2 Mn x2 Te Quantum Dot within the effective mass approximation is carried out employing the variational principle. The results are presented and discussed.

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