223 research outputs found
Fractional Dirac Bracket and Quantization for Constrained Systems
So far, it is not well known how to deal with dissipative systems. There are
many paths of investigation in the literature and none of them present a
systematic and general procedure to tackle the problem. On the other hand, it
is well known that the fractional formalism is a powerful alternative when
treating dissipative problems. In this paper we propose a detailed way of
attacking the issue using fractional calculus to construct an extension of the
Dirac brackets in order to carry out the quantization of nonconservative
theories through the standard canonical way. We believe that using the extended
Dirac bracket definition it will be possible to analyze more deeply gauge
theories starting with second-class systems.Comment: Revtex 4.1. 9 pages, two-column. Final version to appear in Physical
Review
Onsager-Manning-Oosawa condensation phenomenon and the effect of salt
Making use of results pertaining to Painleve III type equations, we revisit
the celebrated Onsager-Manning-Oosawa condensation phenomenon for charged stiff
linear polymers, in the mean-field approximation with salt. We obtain
analytically the associated critical line charge density, and show that it is
severely affected by finite salt effects, whereas previous results focused on
the no salt limit. In addition, we obtain explicit expressions for the
condensate thickness and the electric potential. The case of asymmetric
electrolytes is also briefly addressed.Comment: to appear in Phys. Rev. Let
Ground state energy of the modified Nambu-Goto string
We calculate, using zeta function regularization method, semiclassical energy
of the Nambu-Goto string supplemented with the boundary, Gauss-Bonnet term in
the action and discuss the tachyonic ground state problem.Comment: 10 pages, LaTeX, 2 figure
Exact Quantum Solutions of Extraordinary N-body Problems
The wave functions of Boson and Fermion gases are known even when the
particles have harmonic interactions. Here we generalise these results by
solving exactly the N-body Schrodinger equation for potentials V that can be
any function of the sum of the squares of the distances of the particles from
one another in 3 dimensions. For the harmonic case that function is linear in
r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) =
\zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2
M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the
solution is given in terms of the one or two body problem with potential U(r)
in 3 dimensions. The degeneracies of the levels are derived for distinguishable
particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter
involve significant combinatorial analysis which may have application to the
shell model of atomic nuclei. For large N the Fermionic ground state gives the
binding energy of a degenerate white dwarf star treated as a giant atom with an
N-body wave function. The N-body forces involved in these extraordinary N-body
problems are not the usual sums of two body interactions, but nor are forces
between quarks or molecules. Bose-Einstein condensation of particles in 3
dimensions interacting via these strange potentials can be treated by this
method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal
Societ
Reductions of the Volterra and Toda chains
The Volterra and Toda chains equations are considered. A class of special
reductions for these equations are derived.Comment: LaTeX, 6 page
Quantum toboggans: models exhibiting a multisheeted PT symmetry
A generalization of the concept of PT-symmetric Hamiltonians H=p^2+V(x) is
described. It uses analytic potentials V(x) (with singularities) and a
generalized concept of PT-symmetric asymptotic boundary conditions. Nontrivial
toboggans are defined as integrated along topologically nontrivial paths of
coordinates running over several Riemann sheets of wave functions.Comment: 16 pp, 5 figs. Written version of the talk given during 5th
International Symposium on Quantum Theory and Symmetries, University of
Valladolid, Spain, July 22 - 28 2007, webpage http://tristan.fam.uva.es/~qts
Integrability of one degree of freedom symplectic maps with polar singularities
In this paper, we treat symplectic difference equations with one degree of
freedom. For such cases, we resolve the relation between that the dynamics on
the two dimensional phase space is reduced to on one dimensional level sets by
a conserved quantity and that the dynamics is integrable, under some
assumptions. The process which we introduce is related to interval exchange
transformations.Comment: 10 pages, 2 figure
Differential constraints for the Kaup -- Broer system as a reduction of the 1D Toda lattice
It is shown that some special reduction of infinite 1D Toda lattice gives
differential constraints compatible with the Kaup -- Broer system. A family of
the travelling wave solutions of the Kaup -- Broer system and its higher
version is constructed.Comment: LaTeX, uses IOP styl
On Rank Problems for Planar Webs and Projective Structures
We present old and recent results on rank problems and linearizability of
geodesic planar webs.Comment: 31 pages; LaTeX; corrected the abstract and Introduction; added
reference
Biorthogonal quantum mechanics
The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems. © 2014 IOP Publishing Ltd
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