Variational Functions in Open Systems

This paper looks for an entropy-like quantity having a monotonic time development. In the case of spontaneous emission, the final state usually consists of a single ground state assigning zero to the ordinary expressions for entropy. Thus entropy ceases to be a monotonic measure of the direction of time. The point is illustrated by a simple test case consisting of three levels coupled by spontaneous emission. It is shown how this case allows the definition of a monotonic function. Using the theory of non-Hermitian operators, the paper shows how such a function may be constructed in the general case, and it explores the main consequences of the expressions suggested. The generalization of the entropy concept is found to relate to time-reversal properties of the dynamics. The paper concludes by discussing open questions and possible further explorations.     

A Correlation Among Orthogonality Relation,Variational Principle and Perturbation Theory

It is observed that variationally calculated wavefunctions do not satisfy orthogonality relation when tested for the potentials like anharmonic oscillator and deviated hydrogen atom type. A new approach is suggested using quasi-states only to correlate between variationally calculated wavefunctions and orthogonality relation using perturbation theory considering the anharmonic oscillator example. Analytically expression for energy levels of the anharmonic oscillator are calculated up to the second order. A test for convergency of the perturbation theory is also discussed.     

Generalized Value Distribution for Herglotz Functions and Spectral Theory

We generalize the theory of value distribution for a class of functions defined as boundary values of Herglotz functions, by considering other measures than Lebesgue measure. The link with compositions of Herglotz functions is presented, and precise relations for the associated measures are obtained. We also consider uniformly convergent sequences of Herglotz functions on compact subsets of the upper half-plane, and prove that the corresponding sequence of Herglotz measures and the generalized value distribution of these functions also converge.     

Gaussian Time-Dependent Variational Principle for Bosons

We investigate the Dirac time-dependent variational method for a system of non-ideal Bosons interacting through an arbitrary two body potential. The method produces a set of non-linear time dependent equations for the variational parameters. In particular we have considered small oscillations about equilibrium. We obtain generalized RPA equations that can be understood as interacting quasi-bosons, usually mentioned in the literature as having a gap. The result of this interaction provides us with scattering properties of these quasi-bosons including possible bound-states, which can include zero modes. In fact the zero mode bound state can be interpreted as a new quasi-boson with a gapless dispersion relation. Utilizing these results we discuss a straightforward scheme for introducing temperature.     

A Variational Principle for Thermodynamical Waves

When the dissipative processes are dominant in the system, the assumption of local equilibrium holds good and the space time evolution of irreversible system can be described by the variational principle of GYARMATI. However when imposed changes in the state variables are fast, the system can not be in a state of local equilibrium and to define the nonequilibrium state of the system it is necessary to extend the formalism of classical irreversible thermodynamics. The wave approach of Onsagerian thermodynamics is one such pursuit and is a direct generalization of the original Onsager-Machlup proposition. An important consequence of this theory is that it leads to transport equations with finite propagation velocities, which are referred to as thermodynamical waves. In this note we endeavour to write the appropriate form of GYARMATI'S variational principle for thermodynamical waves.     

Variational Principle for Some Renormalized Measures

We show that some measures suffering from the so-called renormalization group pathologies satisfy a variational principle and that the corresponding limit of the pressure, with boundary conditions in a set of measure 1, is equal to the pressure of the Ising model modulo a scale factor.     

A Variational Principle for Markov Processes

In this note, we first present a result concerning a variational principle for general Markov processes. Then we apply it to spin particle systems to obtain a full form of a variational principle characterizing the stationary Markov laws of the systems. A related extreme decomposition for any stationary distribution of such Markov systems is also given.     

BRST Theory in the Formalism of Variational Tricomplex

Russian Physics Journal - By making use of the variational tricomplex, a covariant procedure is proposed for deriving the classical BRST charge from a given master-action.     

Field Equations of TREDER's Gravitational Theory which are Derivable from a Variational Principle. III

In TREDER 's theory of gravitation the active gravitational (SCHWARZSCHILD ) mass is, generally speaking, different from the inertial (rest) mass of a stationary space-bounded field producing system. We consider a certain class of field equations and show that the relative deviation of the inertial (rest) mass from the SCHWARZSCHILD ian mass is very small (≤1/15).     

A Variational Principle Associated to Positive Tilt Maps

In this paper we establish a variational principle for positive tilt maps. This implies that the Aubry–Mather set exists for positive tilt maps and most of the theory developed by Mather for twist maps now applies for positive tilt maps. Received: 14 May 1996 / Accepted: 30 May 1997     

Variational Principle and Almost Quasilocality for Renormalized Measures

We study the variational principle for some non-Gibbsian measures. We give a necessary and sufficient condition for the validity of the implication zero relative entropy density implies common version of conditional probabilities (so-called second part of the variational principle). Applying this to noisy decimations of the low-temperature phases of the Ising model, we obtain almost sure quasilocality for these measures and the second part of the variational principle. For the projection of low temperature Ising phases on a one-dimensional layer, we also obtain the second part of the variational principle.     

A New Variational Principle for the Fundamental Equations of Classical Physics

In this paper we introduce a variational principle from which the fundamental equations of classical physics can be deduced. This principle permits a sort of unification of the gravitational and the electromagnetic fields. The basic point of this variational principle is that the world-line of a material point is parametrized by a parameter a which carries some physical information, namely it is related to the rest mass and to the charge. In particular, the (inertial) rest mass will not be a property of a material point, but it will be a constant of the motion which is determined by the initial conditions. In this framework the equality between the inertial and gravitational mass can be deduced.     

Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm

We propose the difference discrete variational principle in discrete mechanics and symplectic algorithmwith variable step-length of time in finite duration based upon a noncommutative differential calculus established inthis paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists thediscrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existencein finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodicperturbation. The numerical results are satisfactory.     

Difference Discrete Variational Principle in Discrete Mechanics and Symplectic Algorithm

We propose the difference discrete variational principle in discrete mechanics and symplectic algorithm with variable step-length of time in finite duration based upon a noncommutative differential calculus established in this paper. This approach keeps both symplecticity and energy conservation discretely. We show that there exists the discrete version of the Euler-Lagrange cohomology in these discrete systems. We also discuss the solution existence in finite time-length and its site density in continuous limit, and apply our approach to the pendulum with periodic perturbation. The numerical results are satisfactory.     

A New Principle to Determine the Variational Parameter for the Variational-Cumulant Expansion

The key point of the variational-cumulant expanhon is the determination of the variational parameter. In this paper, we present the improved mean-field hypothesis (IMFH) which is the bdse to determine the parameter. The new method derived from the IMFH shows advantage over previous methods. The critical temperature and some thermal dynamical functions for the Heisenberg model are calculated with the new method.     

A Derivation of the Entropy-Based Relativistic Smoothed Particle Hydrodynamics by Variational Principle

In this work, a second order smoothed particle hydrodynamics is derived for the study of relativistic heavy ion collisions. The hydrodynamical equation of motion is formulated in terms of the variational principle. In order to describe the fluid of high energy density but of low baryon density, the entropy is taken as the base quantity for the interpolation. The smoothed particle hydrodynamics algorithm employed in this study is of the second order, which guarantees better particle consistency. Furthermore, it is shown that the variational principle preserves the translational invariance of the system, and therefore improves the accuracy of the method. A brief discussion on the potential implications of the model in heavy ion physics as well as in general relativity are also presented.     

Computing Partial Transposes and Related Entanglement Functions

The partial transpose (PT) is an important function for entanglement testing and quantification and also for the study of geometrical aspects of the quantum state space. In this article, considering general bipartite and multipartite discrete systems, explicit formulas ready for the numerical implementation of the PT and of related entanglement functions are presented and the Fortran code produced for that purpose is described. What is more, we obtain an analytical expression for the Hilbert-Schmidt entanglement of two-qudit systems and for the associated closest separable state. In contrast to previous works on this matter, we only use the properties of the PT, not applying Lagrange multipliers.