175 research outputs found
On the number of representations providing noiseless subsystems
This paper studies the combinatoric structure of the set of all
representations, up to equivalence, of a finite-dimensional semisimple Lie
algebra. This has intrinsic interest as a previously unsolved problem in
representation theory, and also has applications to the understanding of
quantum decoherence. We prove that for Hilbert spaces of sufficiently high
dimension, decoherence-free subspaces exist for almost all representations of
the error algebra. For decoherence-free subsystems, we plot the function
which is the fraction of all -dimensional quantum systems which
preserve bits of information through DF subsystems, and note that this
function fits an inverse beta distribution. The mathematical tools which arise
include techniques from classical number theory.Comment: 17 pp, 4 figs, accepted for Physical Review
Identical Particles and Permutation Group
Second quantization is revisited and creation and annihilation operators
areshown to be related, on the same footing both to the algebra h(1), and to
the superalgebra osp(1|2) that are shown to be both compatible with Bose and
Fermi statistics.
The two algebras are completely equivalent in the one-mode sector but,
because of grading of osp(1|2), differ in the many-particle case.
The same scheme is straightforwardly extended to the quantum case h_q(1) and
osp_q(1|2).Comment: 8 pages, standard TEX, DFF 205/5/94 Firenz
Q-derivatives, coherent states and squeezing
We show that the q-deformation of the Weyl-Heisenberg (q-WH) algebra naturally arises in discretized systems, coherent states, squeezed states and systems with periodic potential on the lattice. We incorporate the q-WH algebra into the theory of (entire) analytical functions, with applications to theta and Bloch functions
Topological origin of the phase transition in a mean-field model
We argue that the phase transition in the mean-field XY model is related to a
particular change in the topology of its configuration space. The nature of
this topological transition can be discussed on the basis of elementary Morse
theory using the potential energy per particle V as a Morse function. The value
of V where such a topological transition occurs equals the thermodynamic value
of V at the phase transition and the number of (Morse) critical points grows
very fast with the number of particles N. Furthermore, as in statistical
mechanics, also in topology the way the thermodynamic limit is taken is
crucial.Comment: REVTeX, 5 pages, with 1 eps figure included. Some changes in the
text. To appear in Physical Review Letter
Thermalization of a Brownian particle via coupling to low-dimensional chaos
It is shown that a paradigm of classical statistical mechanics --- the
thermalization of a Brownian particle --- has a low-dimensional, deterministic
analogue: when a heavy, slow system is coupled to fast deterministic chaos, the
resultant forces drive the slow degrees of freedom toward a state of
statistical equilibrium with the fast degrees. This illustrates how concepts
useful in statistical mechanics may apply in situations where low-dimensional
chaos exists.Comment: Revtex, 11 pages, no figures
A Topological String: The Rasetti-Regge Lagrangian, Topological Quantum Field Theory, and Vortices in Quantum Fluids
The kinetic part of the Rasetti-Regge action I_{RR} for vortex lines is
studied and links to string theory are made. It is shown that both I_{RR} and
the Polyakov string action I_{Pol} can be constructed with the same field X^mu.
Unlike I_{NG}, however, I_{RR} describes a Schwarz-type topological quantum
field theory. Using generators of classical Lie algebras, I_{RR} is generalized
to higher dimensions. In all dimensions, the momentum 1-form P constructed from
the canonical momentum for the vortex belongs to the first cohomology class
H^1(M,R^m) of the worldsheet M swept-out by the vortex line. The dynamics of
the vortex line thus depend directly on the topology of M. For a vortex ring,
the equations of motion reduce to the Serret-Frenet equations in R^3, and in
higher dimensions they reduce to the Maurer-Cartan equations for so(m).Comment: To appear in Journal of Physics
Comment on Vortex Mass and Quantum Tunneling of Vortices
Vortex mass in Fermi superfluids and superconductors and its influence on
quantum tunneling of vortices are discussed. The vortex mass is essentially
enhanced due to the fermion zero modes in the core of the vortex: the bound
states of the Bogoliubov qiasiparticles localized in the core. These bound
states form the normal component which is nonzero even in the low temperature
limit. In the collisionless regime , the normal component
trapped by the vortex is unbound from the normal component in the bulk
superfluid/superconductors and adds to the inertial mass of the moving vortex.
In the d-wave superconductors, the vortex mass has an additional factor
due to the gap nodes.Comment: 10 pages, no figures, version accepted in JETP Letter
z=3 Lifshitz-Horava model and Fermi-point scenario of emergent gravity
Recently Horava proposed a model for gravity which is described by the
Einstein action in the infrared, but lacks the Lorentz invariance in the
high-energy region where it experiences the anisotropic scaling. We test this
proposal using two condensed matter examples of emergent gravity: acoustic
gravity and gravity emerging in the fermionic systems with Fermi points. We
suggest that quantum hydrodynamics, which together with the quantum gravity is
the non-renormalizable theory, may exhibit the anisotropic scaling in agreement
with the proposal. The Fermi point scenario of emergent general relativity
demonstrates that under general conditions, the infrared Einstein action may be
distorted, i.e. the Horava parameter is not necessarily equal 1 even
in the low energy limit. The consistent theory requires special hierarchy of
the ultra-violet energy scales and the fine-tuning mechanism for the Newton
constant.Comment: 5 pages, no figures, JETP Letters style, version accepted in JETP
Letter
- …