1,102 research outputs found
Inverse problem for the retarded field of an arbitrary moving charge
It is assumed that the Lienard-Wiechert fields of an arbitrary moving charge
is measured or predefined as a function of time. The position of the charge is
calculated as a function of the retarded time.Comment: LaTeX2e, 6 pages, published in Physics Letters
Non-Volkov solutions for a charge in a plane wave
We focus our attention, once again, on the Klein--Gordon and Dirac equations
with a plane-wave field. We recall that for the first time a set of solutions
of these equations was found by Volkov. The Volkov solutions are widely used in
calculations of quantum effects with electrons and other elementary particles
in laser beams. We demonstrate that one can construct sets of solutions which
differ from the Volkov solutions and which may be useful in physical
applications. For this purpose, we show that the transversal charge motion in a
plane wave can be mapped by a special transformation to transversal free
particle motion. This allows us to find new sets of solutions where the
transversal motion is characterized by quantum numbers different from Volkov's
(in the Volkov solutions this motion is characterized by the transversal
momentum). In particular, we construct solutions with semiclassical transversal
charge motion (transversal squeezed coherent states). In addition, we
demonstrate how the plane-wave field can be eliminated from the transversal
charge motion in a more complicated case of the so-called combined
electromagnetic field (a combination of a plane-wave field and constant
colinear electric and magnetic fields). Thus, we find new sets of solutions of
the Klein--Gordon and Dirac equations with the combined electromagnetic field.Comment: LaTex file, 14 page
New solutions of relativistic wave equations in magnetic fields and longitudinal fields
We demonstrate how one can describe explicitly the present arbitrariness in
solutions of relativistic wave equations in external electromagnetic fields of
special form. This arbitrariness is connected to the existence of a
transformation, which reduces effectively the number of variables in the
initial equations. Then we use the corresponding representations to construct
new sets of exact solutions, which may have a physical interest. Namely, we
present new sets of stationary and nonstationary solutions in magnetic field
and in some superpositions of electric and magnetic fields.Comment: 25 pages, LaTex fil
On the Wave Zone of Synchrotron Radiation
The extension of the wave zone of synchrotron radiation is studied.Comment: 6 pages, 1 figur
Two interacting spins in external fields. Four-level systems
In the present article, we consider the so-called two-spin equation that
describes four-level quantum systems. Recently, these systems attract attention
due to their relation to the problem of quantum computation. We study general
properties of the two-spin equation and show that the problem for certain
external backgrounds can be identified with the problem of one spin in an
appropriate background. This allows one to generate a number of exact solutions
for two-spin equations on the basis of already known exact solutions of the
one-spin equation. Besides, we present some exact solutions for the two-spin
equation with an external background different for each spin but having the
same direction. We study the eigenvalue problem for a time-independent spin
interaction and a time-independent external background. A possible analogue of
the Rabi problem for the two-spin equation is defined. We present its exact
solution and demonstrate the existence of magnetic resonances in two specific
frequencies, one of them coinciding with the Rabi frequency, and the other
depending on the rotating field magnitude. The resonance that corresponds to
the second frequency is suppressed with respect to the first one.Comment: 14 page
Darboux transformation for two-level systems
We develop the Darboux procedure for the case of the two-level system. In
particular, it is demonstrated that one can construct the Darboux intertwining
operator that does not violate the specific structure of the equations of the
two-level system, transforming only one real potential into another real
potential. We apply the obtained Darboux transformation to known exact
solutions of the two-level system. Thus, we find three classes of new solutions
for the two-level system and the corresponding new potentials that allow such
solutions.Comment: 10 page
Time Dependent Supersymmetry in Quantum Mechanics
The well-known supersymmetric constructions such as Witten's supersymmetric
quantum mechanics, Spiridonov-Rubakov parasupersymmetric quantum mechanics, and
higher-derivative SUSY of Andrianov et al. are extended to the nonstationary
Schr\"odinger equation. All these constructions are based on the time-dependent
Darboux transformation. The superalgebra over the conventional Lie algebra is
constructed. Examples of time-dependent exactly solvable potentials are given.Comment: Talk given at the 7-th Lomonosov Conference "Problems of Fundamental
Physics", 24-30 August, 1995, see proceedings book (with the minor
corrections) Moscow, 1997, p. 54-6
Aharonov-Bohm Effect in Cyclotron and Synchrotron Radiations
We study the impact of Aharonov-Bohm solenoid on the radiation of a charged
particle moving in a constant uniform magnetic field. With this aim in view,
exact solutions of Klein-Gordon and Dirac equations are found in the
magnetic-solenoid field. Using such solutions, we calculate exactly all the
characteristics of one-photon spontaneous radiation both for spinless and
spinning particle. Considering non-relativistic and relativistic
approximations, we analyze cyclotron and synchrotron radiations in detail.
Radiation peculiarities caused by the presence of the solenoid may be
considered as a manifestation of Aharonov-Bohm effect in the radiation. In
particular, it is shown that new spectral lines appear in the radiation
spectrum. Due to angular distribution peculiarities of the radiation intensity,
these lines can in principle be isolated from basic cyclotron and synchrotron
radiation spectraComment: 38 pages, LaTex fil
Pairing induced superconductivity in holography
We study pairing induced superconductivity in large strongly coupled
systems at finite density using holography. In the weakly coupled dual
gravitational theory the mechanism is conventional BCS theory. An IR hard wall
cut-off is included to ensure that we can controllably address the dynamics of
a single confined Fermi surface. We address in detail the interplay between the
scalar order parameter field and fermion pairing. Adding an explicitly
dynamical scalar operator with the same quantum numbers as the fermion-pair,
the theory experiences a BCS/BEC crossover controlled by the relative scaling
dimensions. We find the novel result that this BCS/BEC crossover exposes
resonances in the canonical expectation value of the scalar operator. This
occurs not only when the scaling dimension is degenerate with the Cooper pair,
but also with that of higher derivative paired operators. We speculate that a
proper definition of the order parameter which takes mixing with these
operators into account stays finite nevertheless.Comment: 38 pages; 24 figures; revtex4 v2: Acknowledgements adde
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