1,713 research outputs found
On the two-magnon bound states for the quantum Heisenberg chain with variable range exchange
The spectrum of finite-difference two-magnon operator is investigated for
quantum S=1/2 chain with variable range exchange of the form . It is found that usual bound state appears for some values
of the total pseudomomentum of two magnons as for the Heisenberg chain with
nearest-neighbor spin interaction. Besides this state, a new type of bound
state with oscillating wave function appears at larger values of the total
pseudomomentum.Comment: 8 pages, latex, no figure
Spectral correlations in systems undergoing a transition from periodicity to disorder
We study the spectral statistics for extended yet finite quasi 1-d systems
which undergo a transition from periodicity to disorder. In particular we
compute the spectral two-point form factor, and the resulting expression
depends on the degree of disorder. It interpolates smoothly between the two
extreme limits -- the approach to Poissonian statistics in the (weakly)
disordered case, and the universal expressions derived for the periodic case.
The theoretical results agree very well with the spectral statistics obtained
numerically for chains of chaotic billiards and graphs.Comment: 16 pages, Late
Can chaos be observed in quantum gravity?
Full general relativity is almost certainly 'chaotic'. We argue that this
entails a notion of nonintegrability: a generic general relativistic model, at
least when coupled to cosmologically interesting matter, likely possesses
neither differentiable Dirac observables nor a reduced phase space. It follows
that the standard notion of observable has to be extended to include
non-differentiable or even discontinuous generalized observables. These cannot
carry Poisson-algebraic structures and do not admit a standard quantization;
one thus faces a quantum representation problem of gravitational observables.
This has deep consequences for a quantum theory of gravity, which we
investigate in a simple model for a system with Hamiltonian constraint that
fails to be completely integrable. We show that basing the quantization on
standard topology precludes a semiclassical limit and can even prohibit any
solutions to the quantum constraints. Our proposed solution to this problem is
to refine topology such that a complete set of Dirac observables becomes
continuous. In the toy model, it turns out that a refinement to a polymer-type
topology, as e.g. used in loop gravity, is sufficient. Basing quantization of
the toy model on this finer topology, we find a complete set of quantum Dirac
observables and a suitable semiclassical limit. This strategy is applicable to
realistic candidate theories of quantum gravity and thereby suggests a solution
to a long-standing problem which implies ramifications for the very concept of
quantization. Our work reveals a qualitatively novel facet of chaos in physics
and opens up a new avenue of research on chaos in gravity which hints at deep
insights into the structure of quantum gravity.Comment: 6 pages + references -- matches published version (clarifications
added for why GR with cosmologically interesting matter likely fails our
notion of weak-integrability
Non-adiabatic pumping in an oscillating-piston model
We consider the prototypical "piston pump" operating on a ring, where a
circulating current is induced by means of an AC driving. This can be regarded
as a generalized Fermi-Ulam model, incorporating a finite-height moving wall
(piston) and non trivial topology (ring). The amount of particles transported
per cycle is determined by a layered structure of phase-space. Each layer is
characterized by a different drift velocity. We discuss the differences
compared with the adiabatic and Boltzmann pictures, and highlight the
significance of the "diabatic" contribution that might lead to a
counter-stirring effect.Comment: 6 pages, 4 figures, improved versio
Optical probes of the quantum vacuum: The photon polarization tensor in external fields
The photon polarization tensor is the central building block of an effective
theory description of photon propagation in the quantum vacuum. It accounts for
the vacuum fluctuations of the underlying theory, and in the presence of
external electromagnetic fields, gives rise to such striking phenomena as
vacuum birefringence and dichroism. Standard approximations of the polarization
tensor are often restricted to on-the-light-cone dynamics in homogeneous
electromagnetic fields, and are limited to certain momentum regimes only. We
devise two different strategies to go beyond these limitations: First, we aim
at obtaining novel analytical insights into the photon polarization tensor for
homogeneous fields, while retaining its full momentum dependence. Second, we
employ wordline numerical methods to surpass the constant-field limit.Comment: 13 pages, 4 figures; typo in Eq. (5) corrected (matches journal
version
Short wavelength quantum electrodynamical correction to cold plasma-wave propagation
The effect of short wavelength quantum electrodynamic (QED) correction on
plasma-wave propagation is investigated. The effect on plasma oscillations and
on electromagnetic waves in an unmagnetized as well as a magnetized plasma is
investigated. The effects of the short wavelength QED corrections are most
significant for plasma oscillations and for extraordinary modes. In particular,
the QED correction allow plasma oscillations to propagate, and the
extra-ordinary mode looses its stop band. The significance of our results is
discussed.Comment: 12 pages, 5 figure
Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]
Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for
convergent series representations of both the real and the imaginary part of
the QED effective action; these derivations were based on correct intermediate
steps. In this comment, we argue that the physical significance of the
"logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86,
1947 (2001)] in comparison to the usual expression for the QED effective action
remains to be demonstrated. Further information on related subjects can be
found in Appendix A of hep-ph/0308223 and in hep-th/0210240.Comment: 1 page, RevTeX; only "meta-data" update
Directed Chaotic Transport in Hamiltonian Ratchets
We present a comprehensive account of directed transport in one-dimensional
Hamiltonian systems with spatial and temporal periodicity. They can be
considered as Hamiltonian ratchets in the sense that ensembles of particles can
show directed ballistic transport in the absence of an average force. We
discuss general conditions for such directed transport, like a mixed classical
phase space, and elucidate a sum rule that relates the contributions of
different phase-space components to transport with each other. We show that
regular ratchet transport can be directed against an external potential
gradient while chaotic ballistic transport is restricted to unbiased systems.
For quantized Hamiltonian ratchets we study transport in terms of the evolution
of wave packets and derive a semiclassical expression for the distribution of
level velocities which encode the quantum transport in the Floquet band
spectra. We discuss the role of dynamical tunneling between transporting
islands and the chaotic sea and the breakdown of transport in quantum ratchets
with broken spatial periodicity.Comment: 22 page
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