A mechanical approach to one-dimensional interacting gas

Derivations of the van der Waals equation typically use standard recipes involving ensemble averages of statistical mechanics. In this work, we study a box of weakly interacting gas particles in one-dimension by explicitly incorporating the mechanical point of view. This has the merit that it not only reproduces the van der Waals equation but also tells us some extra interesting physics not immediately clear from a pure statistical mechanical approach. For example, we show that the traditional handwaving argument leading to van der Waals equation requires closer scrutiny if it is to get things right.     

A new variational approach to the hydrogen atom in magnetic fields

We develop a simple and useful variational method to obtain approximate eigenenergies and expectation values ofr ² andρ ² for a hydrogenlike atom in a magnetic field. Results agree quite well with accurate numerically computed ones in the whole range of field intensities.     

Remarks on some new models of interacting quantum fields with indefinite metric

We study quantum field models in indefinite metric. We introduce the modified Wightman axioms of Morchio and Strocchi as a general framework of indefinite metric quantum field theory (QFT) and present concrete interacting relativistic models obtained by analytical continuation from some stochastic processes with Euclidean invariance. As a first step towards scattering theory in indefinite metric QFT, we give a proof of the spectral condition on the translation group for the relativistic models.     

A covariant approach to gauged 2D self-dual fields

We obtain a non-Abelian version of a theory involving vector and tensor gauge fields interacting via a massive topological coupling, besides the nonminimun one. The new fact is that the non-Abelian theory is not reducible and Stuckelberg fields are introduced in order to make compatible gauge invariance, nontrivial physical degrees of freedom and the limit of the Abelian case.     

On conformal invariance of interacting fields

We study the action of the conformal algebra on interacting fields. On a certain set of states the algebra is integrated to projective representations ofSU(2,2). These representations are shown to be equivalent to the representations of the interpolated discrete series ofSU(2,2). Using this result we give a formula for the two-point Wightman function for arbitrary spin and dimension of the field. Finally we discuss the limit when the dimension tends to the canonical value.     

A new approach to particle confinement

A new approach to permanent confinement of non-relativistic and relativistic particles inside microscopic regions of space is presented. Motion in suitably chosen energy-dependent potentials turns out to be such that the size of orbits of particles bound in such potentials decreases when energy is supplied to them from external sources and there exists a maximum size of these orbits. The energy spectrum is purely discrete without any continuum. The dynamics of such particles requires the introduction of a space-dependent metric in the Hilbert space of states to ensure conservation of probability.     

A new approach to computer holography

Instead of encoding the object wavefront at N₀ points, we encode a new wavefront which has near-unity intensity at N₁ (⪡ N₀) of those points and is zero elsewhere. Significant savings in plotting time and in dynamic range requirements result.     

A new approach to classical mechanics

A new approach to classical mechanics proposed by Prigogine, George, and Rae, which avoids the nonlinear Hamilton-Jacobi technique and introduces a linear eigenvalue problem involving probabilities as eigenvectors, is illustrated by the study of an exactly soluble model.     

A new approach to nonrenormalizable models

Nonrenormalizable quantum field theories require counter-terms; and based on the hard-core interpretation of such interactions, it is initially argued, contrary to the standard view, that counter-terms suggested by renormalized perturbation theory are in fact inappropriate for this purpose. Guided by the potential underlying causes of triviality of such models, as obtained by alternative analyses, we focus attention on the ground-state distribution function, and suggest a formulation of such distributions that exhibits nontriviality from the start. Primary discussion is focused on self-interacting scalar fields. Conditions for bounds on general correlation functions are derived, and there is some discussion of the issues involved with the continuum limit.     

A new approach to potential scattering

Potential scattering calculations based onCalogero's equation and given in two former papers are now improved to include unitarity of theS-matrix. It is shown that the method gives results better than the second Born approximation and even reasonable in the two limits of very strong coupling and very low energies. As test examples, the square-well potential and the Yukawa potential are discussed.     

A new approach to peratization technique

The usual method of peratization technique is to expand scattering lengthA(a) in Born series in powers of the coupling constantg. In this paper a new approach to the peratization technique has been discussed starting with the standard equation for the scattering length. As an application of the theory developed, the cases of inverse fourth power and a logarithmic singular potentials have been discussed.     

A new approach to potential scattering

An approximate integral-representation of theS-matrix in partial-wave expansion is derived for a scalar Schrödinger particle in a central field. The method consists of linearizingCalogero's Riccati equation for the interpolatingS-matrix in such a way that the solution of the linearized equation deviates as little as possible from the exact one. TheS-matrix thus obtained exhibits exact crossing-symmetry and uniform convergence independent of the coupling constant of the scattering potential. In the weak coupling limit it is especially shown thatour method is more accurate than the second Born approximation. In the second part of the paper we specialize ourS-matrix to low and large energies. At low energies, a general integral for the scattering length is obtained and at large energies the summation over all angular momenta is carried out yielding an expression for the scattering amplitude.     

Helium atom in intense and superintense laser fields: A new theoretical approach

A quantum hydrodynamical study is made of the dynamical changes of a helium atom interacting with lasers of two different intensities, but having the same frequency. Under the intense laser field, electron density oozes out of the helium atom by absorbing laser photons and getting promoted to higher excited states including the continuum. Under the superintense field, electron density partly moves away from the helium nucleus but remains in the “quasi-bound” dressed states along with the laser field, thus suppressing ionization.     

A direct variational approach to Skyrme's model for meson fields

The solutions of Skyrme's variational problem describe the structure of mesons in a field of weak energy. The problem consists in minimizing the corresponding energy among the functions from ³ toS ³ which have a fixed degree without making any symmetry assumptions. We prove the existence of minima and study their properties.     

A new mathematical problem related to quantization of fields

This paper is a survey of author??s mathematical and logical studies concerning the quantization of fields.     

Two interacting spins in external fields and application to quantum computation

We study the four-level-system given by two quantum dots immersed in a time-dependent magnetic field, which are coupled to each other by an effective Heisenberg-type interaction. We describe the construction of the corresponding evolution operator in a special case of different time-dependent parallel external magnetic fields. We find a relation between the external field and the effective interaction function. The obtained results are used to analyze the theoretical implementation of a universal quantum gate.