395 research outputs found
Variational principle for the Wheeler-Feynman electrodynamics
We adapt the formally-defined Fokker action into a variational principle for
the electromagnetic two-body problem. We introduce properly defined boundary
conditions to construct a Poincare-invariant-action-functional of a finite
orbital segment into the reals. The boundary conditions for the variational
principle are an endpoint along each trajectory plus the respective segment of
trajectory for the other particle inside the lightcone of each endpoint. We
show that the conditions for an extremum of our functional are the
mixed-type-neutral-equations with implicit state-dependent-delay of the
electromagnetic-two-body problem. We put the functional on a natural Banach
space and show that the functional is Frechet-differentiable. We develop a
method to calculate the second variation for C2 orbital perturbations in
general and in particular about circular orbits of large enough radii. We prove
that our functional has a local minimum at circular orbits of large enough
radii, at variance with the limiting Kepler action that has a minimum at
circular orbits of arbitrary radii. Our results suggest a bifurcation at some
radius below which the circular orbits become saddle-point extrema. We give a
precise definition for the distributional-like integrals of the Fokker action
and discuss a generalization to a Sobolev space of trajectories where the
equations of motion are satisfied almost everywhere. Last, we discuss the
existence of solutions for the state-dependent delay equations with slightly
perturbated arcs of circle as the boundary conditions and the possibility of
nontrivial solenoidal orbits
Kinematics and hydrodynamics of spinning particles
In the first part (Sections 1 and 2) of this paper --starting from the Pauli
current, in the ordinary tensorial language-- we obtain the decomposition of
the non-relativistic field velocity into two orthogonal parts: (i) the
"classical part, that is, the 3-velocity w = p/m OF the center-of-mass (CM),
and (ii) the so-called "quantum" part, that is, the 3-velocity V of the motion
IN the CM frame (namely, the internal "spin motion" or zitterbewegung). By
inserting such a complete, composite expression of the velocity into the
kinetic energy term of the non-relativistic classical (i.e., newtonian)
lagrangian, we straightforwardly get the appearance of the so-called "quantum
potential" associated, as it is known, with the Madelung fluid. This result
carries further evidence that the quantum behaviour of micro-systems can be
adirect consequence of the fundamental existence of spin. In the second part
(Sections 3 and 4), we fix our attention on the total 3-velocity v = w + V, it
being now necessary to pass to relativistic (classical) physics; and we show
that the proper time entering the definition of the four-velocity v^mu for
spinning particles has to be the proper time tau of the CM frame. Inserting the
correct Lorentz factor into the definition of v^mu leads to completely new
kinematical properties for v_mu v^mu. The important constraint p_mu v^mu = m,
identically true for scalar particles, but just assumed a priori in all
previous spinning particle theories, is herein derived in a self-consistent
way.Comment: LaTeX file; needs kapproc.st
Relativistic two-body system in (1+1)-dimensions
The relativistic two-body system in (1+1)-dimensional quantum electrodynamics
is studied. It is proved that the eigenvalue problem for the two-body
Hamiltonian without the self-interaction terms reduces to the problem of
solving an one-dimensional stationary Schr\"odinger type equation with an
energy-dependent effective potential which includes the delta-functional and
inverted oscillator parts. The conditions determining the metastable energy
spectrum are derived, and the energies and widths of the metastable levels are
estimated in the limit of large particle masses. The effects of the
self-interaction are discussed.Comment: LATEX file, 21 pp., 4 figure
Einstein-Podolsky-Rosen-Bohm experiment with relativistic massive particles
The EPRB experiment with massive partcles can be formulated if one defines
spin in a relativistic way. Two versions are discussed: The one using the spin
operator defined via the relativistic center-of-mass operator, and the one
using the Pauli-Lubanski vector. Both are shown to lead to the SAME prediction
for the EPRB experiment: The degree of violation of the Bell inequality
DECREASES with growing velocity of the EPR pair of spin-1/2 particles. The
phenomenon can be physically understood as a combined effect of the Lorentz
contraction and the Moller shift of the relativistic center of mass. The effect
is therefore stronger than standard relativistic phenomena such as the Lorentz
contraction or time dilatation. The fact that the Bell inequality is in general
less violated than in the nonrelativistic case will have to be taken into
account in tests for eavesdropping if massive particles will be used for a key
transfer.Comment: Figures added as appeared in PRA, two typos corrected (one important
in the formula for eigenvector in Sec. IV); link to the unpublished 1984
paper containing the results (without typos!) of Sec. IV is adde
On the squeezed states for n observables
Three basic properties (eigenstate, orbit and intelligence) of the canonical
squeezed states (SS) are extended to the case of arbitrary n observables. The
SS for n observables X_i can be constructed as eigenstates of their linear
complex combinations or as states which minimize the Robertson uncertainty
relation. When X_i close a Lie algebra L the generalized SS could also be
introduced as orbit of Aut(L^C). It is shown that for the nilpotent algebra h_N
the three generalizations are equivalent. For the simple su(1,1) the family of
eigenstates of uK_- + vK_+ (K_\pm being lowering and raising operators) is a
family of ideal K_1-K_2 SS, but it cannot be represented as an Aut(su^C(1,1))
orbit although the SU(1,1) group related coherent states (CS) with symmetry are
contained in it.
Eigenstates |z,u,v,w;k> of general combination uK_- + vK_+ + wK_3 of the
three generators K_j of SU(1,1) in the representations with Bargman index k =
1/2,1, ..., and k = 1/4,3/4 are constructed and discussed in greater detail.
These are ideal SS for K_{1,2,3}. In the case of the one mode realization of
su(1,1) the nonclassical properties (sub-Poissonian statistics, quadrature
squeezing) of the generalized even CS |z,u,v;+> are demonstrated. The states
|z,u,v,w;k=1/4,3/4> can exhibit strong both linear and quadratic squeezing.Comment: 25 pages, LaTex, 4 .pic and .ps figures. Improvements in text,
discussion on generation scheme added. To appear in Phys. Script
Generation of single-mode SU(1,1) intelligent states and an analytic approach to their quantum statistical properties
We discuss a scheme for generation of single-mode photon states associated
with the two-photon realization of the SU(1,1) algebra. This scheme is based on
the process of non-degenerate down-conversion with the signal prepared
initially in the squeezed vacuum state and with a measurement of the photon
number in one of the output modes. We focus on the generation and properties of
single-mode SU(1,1) intelligent states which minimize the uncertainty relations
for Hermitian generators of the group. Properties of the intelligent states are
studied by using a ``weak'' extension of the analytic representation in the
unit disk. Then we are able to obtain exact analytical expressions for
expectation values describing quantum statistical properties of the SU(1,1)
intelligent states. Attention is mainly devoted to the study of photon
statistics and linear and quadratic squeezing.Comment: to appear in Quantum Semiclass. Opt., LaTeX, epsf style, 21 pages
including 5 Postscript figures. More information on
http://www.technion.ac.il/~brif/science.htm
Superluminal X-shaped beams propagating without distortion along a coaxial guide
In a previous paper [Phys. Rev. E64 (2001) 066603; e-print physics/0001039],
we showed that localized Superluminal solutions to the Maxwell equations exist,
which propagate down (non-evanescence) regions of a metallic cylindrical
waveguide. In this paper we construct analogous non-dispersive waves
propagating along coaxial cables. Such new solutions, in general, consist in
trains of (undistorted) Superluminal "X-shaped" pulses. Particular attention is
paid to the construction of finite total energy solutions. Any results of this
kind may find application in the other fields in which an essential role is
played by a wave-equation (like acoustics, geophysics, etc.). [PACS nos.:
03.50.De; 41.20;Jb; 83.50.Vr; 62.30.+d; 43.60.+d; 91.30.Fn; 04.30.Nk; 42.25.Bs;
46.40.Cd; 52.35.Lv. Keywords: Wave equations; Wave propagation; Localized
beams; Superluminal waves; Coaxial cables; Bidirectional decomposition; Bessel
beams; X-shaped waves; Maxwell equations; Microwaves; Optics; Special
relativity; Coaxial metallic waveguides; Acoustics; Seismology; Mechanical
waves; Elastic waves; Guided gravitational waves.]Comment: plain LaTeX file (22 pages), plus 15 figures; in press in Phys. Rev.
Covariant Equilibrium Statistical Mechanics
A manifest covariant equilibrium statistical mechanics is constructed
starting with a 8N dimensional extended phase space which is reduced to the 6N
physical degrees of freedom using the Poincare-invariant constrained
Hamiltonian dynamics describing the micro-dynamics of the system. The reduction
of the extended phase space is initiated forcing the particles on energy shell
and fixing their individual time coordinates with help of invariant time
constraints. The Liouville equation and the equilibrium condition are
formulated in respect to the scalar global evolution parameter which is
introduced by the time fixation conditions. The applicability of the developed
approach is shown for both, the perfect gas as well as the real gas. As a
simple application the canonical partition integral of the monatomic perfect
gas is calculated and compared with other approaches. Furthermore,
thermodynamical quantities are derived. All considerations are shrinked on the
classical Boltzmann gas composed of massive particles and hence quantum effects
are discarded.Comment: 22 pages, 1 figur
Coherent states for the hydrogen atom: discrete and continuous spectra
We construct the systems of generalised coherent states for the discrete and
continuous spectra of the hydrogen atom. These systems are expressed in
elementary functions and are invariant under the (discrete spectrum)
and (continuous spectrum) subgroups of the dynamical symmetry group
of the hydrogen atom. Both systems of coherent states are particular
cases of the kernel of integral operator which interwines irreducible
representations of the group.Comment: 15 pages, LATEX, minor sign corrections, to appear in J.Phys.
Universal Algorithm for Optimal Estimation of Quantum States from Finite Ensembles
We present a universal algorithm for the optimal quantum state estimation of
an arbitrary finite dimensional system. The algorithm specifies a physically
realizable positive operator valued measurement (POVM) on a finite number of
identically prepared systems. We illustrate the general formalism by applying
it to different scenarios of the state estimation of N independent and
identically prepared two-level systems (qubits).Comment: 4 pages, RevTeX, minor modifications to the tex
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