227 research outputs found
Boson-fermion mapping and dynamical supersymmetry in fermion models
We show that a dynamical supersymmetry can appear in a purely fermionic
system. This ``supersymmetry without bosons" is constructed by application of a
recently introduced boson-fermion Dyson mapping from a fermion space to a space
comprised of collective bosons and ideal fermions. In some algebraic fermion
models of nuclear structure, particular Hamiltonians may lead to collective
spectra of even and odd nuclei that can be unified using the dynamical
supersymmetry concept with Pauli correlations exactly taken into account.Comment: 20 pages. Revtex. One PostScript figure available on request from P
Interaction via reduction and nonlinear superconformal symmetry
We show that the reduction of a planar free spin-1/2 particle system by the
constraint fixing its total angular momentum produces the one-dimensional
Akulov-Pashnev-Fubini-Rabinovici superconformal mechanics model with the
nontrivially coupled boson and fermion degrees of freedom. The modification of
the constraint by including the particle's spin with the relative weight , , and subsequent application of the Dirac reduction procedure (`first
quantize and then reduce') give rise to the anomaly free quantum system with
the order nonlinear superconformal symmetry constructed recently in
hep-th/0304257. We establish the origin of the quantum corrections to the
integrals of motion generating the nonlinear superconformal algebra, and fix
completely its form.Comment: 12 pages; typos correcte
Superconformal mechanics and nonlinear supersymmetry
We show that a simple change of the classical boson-fermion coupling
constant, , , in the superconformal mechanics
model gives rise to a radical change of a symmetry: the modified classical and
quantum systems are characterized by the nonlinear superconformal symmetry. It
is generated by the four bosonic integrals which form the so(1,2) x u(1)
subalgebra, and by the 2(n+1) fermionic integrals constituting the two spin-n/2
so(1,2)-representations and anticommuting for the order n polynomials of the
even generators. We find that the modified quantum system with an integer value
of the parameter is described simultaneously by the two nonlinear
superconformal symmetries of the orders relatively shifted in odd number. For
the original quantum model with , , this means the
presence of the order 2p nonlinear superconformal symmetry in addition to the
osp(2|2) supersymmetry.Comment: 16 pages; misprints corrected, note and ref added, to appear in JHE
Symmetry classes of disordered fermions
Building upon Dyson's fundamental 1962 article known in random-matrix theory
as 'the threefold way', we classify disordered fermion systems with quadratic
Hamiltonians by their unitary and antiunitary symmetries. Important examples
are afforded by noninteracting quasiparticles in disordered metals and
superconductors, and by relativistic fermions in random gauge field
backgrounds.
The primary data of the classification are a Nambu space of fermionic field
operators which carry a representation of some symmetry group. Our approach is
to eliminate all of the unitary symmetries from the picture by transferring to
an irreducible block of equivariant homomorphisms. After reduction, the block
data specifying a linear space of symmetry-compatible Hamiltonians consist of a
basic vector space V, a space of endomorphisms in End(V+V*), a bilinear form on
V+V* which is either symmetric or alternating, and one or two antiunitary
symmetries that may mix V with V*. Every such set of block data is shown to
determine an irreducible classical compact symmetric space. Conversely, every
irreducible classical compact symmetric space occurs in this way.
This proves the correspondence between symmetry classes and symmetric spaces
conjectured some time ago.Comment: 52 pages, dedicated to Freeman J. Dyson on the occasion of his 80th
birthda
On the quantum description of Einstein's Brownian motion
A fully quantum treatment of Einstein's Brownian motion is given, showing in
particular the role played by the two original requirements of translational
invariance and connection between dynamics of the Brownian particle and atomic
nature of the medium. The former leads to a clearcut relationship with Holevo's
result on translation-covariant quantum-dynamical semigroups, the latter to a
formulation of the fluctuation-dissipation theorem in terms of the dynamic
structure factor, a two-point correlation function introduced in seminal work
by van Hove, directly related to density fluctuations in the medium and
therefore to its atomistic, discrete nature. A microphysical expression for the
generally temperature dependent friction coefficient is given in terms of the
dynamic structure factor and of the interaction potential describing the single
collisions. A comparison with the Caldeira Leggett model is drawn, especially
in view of the requirement of translational invariance, further characterizing
general structures of reduced dynamics arising in the presence of symmetry
under translations.Comment: 14 pages, latex, no figure
- …