Photon Green's function and the Casimir energy in a medium

A new expansion is established for the Green's function of the electromagnetic field in a medium with arbitrary $\epsilon$ and $\mu$. The obtained Born series are shown to consist of two types of interactions - the usual terms (denoted $\cal P$) that appear in the Lifshitz theory combined with a new kind of terms (which we denote by $\cal Q$) associated with the changes in the permeability of the medium. Within this framework the case of uniform velocity of light ($\epsilon\mu={\rm const}$) is studied. We obtain expressions for the Casimir energy density and the first non-vanishing contribution is manipulated to a simplified form. For (arbitrary) spherically symmetric $\mu$ we obtain a simple expression for the electromagnetic energy density, and as an example we obtain from it the Casimir energy of a dielectric-diamagnetic ball. It seems that the technique presented can be applied to a variety of problems directly, without expanding the eigenmodes of the problem and using boundary condition considerations

Tunneling and the Band Structure of Chaotic Systems

We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex orbits. These turn out to be fundamental for a proper description of the band structure since they incorporate conduction processes through tunneling mechanisms. The results obtained, illustrated with the kicked-Harper model, are in excellent agreement with numerical simulations, even in the extreme quantum regime.Comment: 11 pages, Latex, figures on request to the author (to be sent by fax

Extended Gibbs ensembles with flow

A statistical treatment of finite unbound systems in the presence of collective motions is presented and applied to a classical Lennard-Jones Hamiltonian, numerically simulated through molecular dynamics. In the ideal gas limit, the flow dynamics can be exactly re-casted into effective time-dependent Lagrange parameters acting on a standard Gibbs ensemble with an extra total energy conservation constraint. Using this same ansatz for the low density freeze-out configurations of an interacting expanding system, we show that the presence of flow can have a sizeable effect on the microstate distribution.Comment: 7 pages, 4 figure

З історії контрольно-насіннєвої справи в Україні: значення і роль М. М. Кулешова у її становленні (1908–1926)

It covers the activities of the scientist-grower N.N. Kuleshov (1890–1968) in the context of the development of domestic control of seeds. It is not only deeply versed in the theoretical and practical problems of seed production and selection, but also the main principles of the organization and functioning of the control system. He made a significant contribution to its formation: Central led the seed of the Ukrainian SSR station, worked on the Kharkov Plant Breeding Station, participated in the All-Ukrainian Society of seed, congresses and meetings, developed a core program based on scientific and research activities of seed control stations. Along with other important problems crop area selection, seed were one of the major in its activities, especially in the first half of the work.Отражена деятельность ученого-растениевода М.М. Кулешова (1890–1968) в контексте развития отечественного контрольно-семенного дела. Он не только глубоко разбирался в теоретических и практических проблемах семеноводства и селекции, но и в главных принципах организации и функционирования системы контроля. Сделал весомый вклад в ее становление: возглавлял Центральную семенную станцию УССР, работал на Харьковской селекционной станции, участвовал в работе Всеукраинского общества семеноводства, съездах и совещаниях, разрабатывал основные программные основы научно-исследовательской деятельности семенных контрольных станций. Наряду с другими важными проблемами растениеводства, направление селекции, семеноводства, сортоведения были главными в его деятельности, особенно в первой половине его творческого пути.Висвітлено діяльність вченого-рослинника М.М. Кулешова (1890–1968) у контексті розбудови вітчизняної контрольно-насіннєвої справи. Він не тільки глибоко розумівся на теоретичних і практичних проблемах насінництва і селекції, а й на головних засадах організації та функціонування системи контролю. Зробив вагомий внесок у її становлення: очолював Центральну насіннєву станцію УРСР, працював на Харківській селекційній станції, брав участь у роботі Всеукраїнського товариства насінництва, з’їздах і нарадах, розробляв основні програмні засади науково-дослідної діяльності насіннєвих контрольних станцій. Поряд з іншими важливими проблемами рослинництва напрями селекції, насінництва, сортознавства були одними з основних у його діяльності, особливо у першій половині творчості

Semiclassical Casimir Energies at Finite Temperature

We study the dependence on the temperature T of Casimir effects for a range of systems, and in particular for a pair of ideal parallel conducting plates, separated by a vacuum. We study the Helmholtz free energy, combining Matsubara's formalism, in which the temperature appears as a periodic Euclidean fourth dimension of circumference 1/T, with the semiclassical periodic orbital approximation of Gutzwiller. By inspecting the known results for the Casimir energy at T=0 for a rectangular parallelepiped, one is led to guess at the expression for the free energy of two ideal parallel conductors without performing any calculation. The result is a new form for the free energy in terms of the lengths of periodic classical paths on a two-dimensional cylinder section. This expression for the free energy is equivalent to others that have been obtained in the literature. Slightly extending the domain of applicability of Gutzwiller's semiclassical periodic orbit approach, we evaluate the free energy at T>0 in terms of periodic classical paths in a four-dimensional cavity that is the tensor product of the original cavity and a circle. The validity of this approach is at present restricted to particular systems. We also discuss the origin of the classical form of the free energy at high temperatures.Comment: 17 pages, no figures, Late

Periodic Orbit Quantization beyond Semiclassics

A quantum generalization of the semiclassical theory of Gutzwiller is given. The new formulation leads to systematic orbit-by-orbit inclusion of higher $\hbar$ contributions to the spectral determinant. We apply the theory to billiard systems, and compare the periodic orbit quantization including the first $\hbar$ contribution to the exact quantum mechanical results.Comment: revte

Quasiclassical Random Matrix Theory

We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN unitary matrix, is considered to be a random matrix. Rather than rejecting all knowledge of the system, except for its symmetry, [as with Dyson's circular unitary ensemble], we choose an ensemble which incorporates the knowledge of the shortest periodic orbits, the prime quasiclassical information bearing on the spectrum. The results largely agree with expectations but contain novel features differing from other recent theories.Comment: 4 pages, RevTex, submitted to Phys. Rev. Lett., permanent e-mail [email protected]

Heat kernel of integrable billiards in a magnetic field

We present analytical methods to calculate the magnetic response of non-interacting electrons constrained to a domain with boundaries and submitted to a uniform magnetic field. Two different methods of calculation are considered - one involving the large energy asymptotic expansion of the resolvent (Stewartson-Waechter method) is applicable to the case of separable systems, and another based on the small time asymptotic behaviour of the heat kernel (Balian-Bloch method). Both methods are in agreement with each other but differ from the result obtained previously by Robnik. Finally, the Balian-Bloch multiple scattering expansion is studied and the extension of our results to other geometries is discussed.Comment: 13 pages, Revte

Berry's conjecture and information theory

It is shown that, by applying a principle of information theory, one obtains Berry's conjecture regarding the high-lying quantal energy eigenstates of classically chaotic systems.Comment: 8 pages, no figure

Boundary dynamics and multiple reflection expansion for Robin boundary conditions

In the presence of a boundary interaction, Neumann boundary conditions should be modified to contain a function S of the boundary fields: (\nabla_N +S)\phi =0. Information on quantum boundary dynamics is then encoded in the $S$-dependent part of the effective action. In the present paper we extend the multiple reflection expansion method to the Robin boundary conditions mentioned above, and calculate the heat kernel and the effective action (i) for constant S, (ii) to the order S^2 with an arbitrary number of tangential derivatives. Some applications to symmetry breaking effects, tachyon condensation and brane world are briefly discussed.Comment: latex, 22 pages, no figure