93 research outputs found
Reduction of Lie--Jordan algebras: Quantum
In this paper we present a theory of reduction of quantum systems in the
presence of symmetries and constraints. The language used is that of
Lie--Jordan Banach algebras, which are discussed in some detail together with
spectrum properties and the space of states. The reduced Lie--Jordan Banach
algebra is characterized together with the Dirac states on the physical algebra
of observables
Coherent wave transmission in quasi-one-dimensional systems with L\'evy disorder
We study the random fluctuations of the transmission in disordered
quasi-one-dimensional systems such as disordered waveguides and/or quantum
wires whose random configurations of disorder are characterized by density
distributions with a long tail known as L\'evy distributions. The presence of
L\'evy disorder leads to large fluctuations of the transmission and anomalous
localization, in relation to the standard exponential localization (Anderson
localization). We calculate the complete distribution of the transmission
fluctuations for different number of transmission channels in the presence and
absence of time-reversal symmetry. Significant differences in the transmission
statistics between disordered systems with Anderson and anomalous localizations
are revealed. The theoretical predictions are independently confirmed by tight
binding numerical simulations.Comment: 10 pages, 6 figure
Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems
We work out finite-dimensional integral formulae for the scalar product of
genus one states of the group Chern-Simons theory with insertions of Wilson
lines. Assuming convergence of the integrals, we show that unitarity of the
elliptic Knizhnik-Zamolodchikov-Bernard connection with respect to the scalar
product of CS states is closely related to the Bethe Ansatz for the commuting
Hamiltonians building up the connection and quantizing the quadratic
Hamiltonians of the elliptic Hitchin system.Comment: 24 pages, latex fil
On the M\"obius transformation in the entanglement entropy of fermionic chains
There is an intimate relation between entanglement entropy and Riemann
surfaces. This fact is explicitly noticed for the case of quadratic fermionic
Hamiltonians with finite range couplings. After recollecting this fact, we make
a comprehensive analysis of the action of the M\"obius transformations on the
Riemann surface. We are then able to uncover the origin of some symmetries and
dualities of the entanglement entropy already noticed recently in the
literature. These results give further support for the use of entanglement
entropy to analyse phase transition.Comment: 29 pages, 5 figures. Final version published in JSTAT. Two new
figures. Some comments and references added. Typos correcte
Entanglement in fermionic chains with finite range coupling and broken symmetries
We obtain a formula for the determinant of a block Toeplitz matrix associated
with a quadratic fermionic chain with complex coupling. Such couplings break
reflection symmetry and/or charge conjugation symmetry. We then apply this
formula to compute the Renyi entropy of a partial observation to a subsystem
consisting of contiguous sites in the limit of large . The present work
generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A
striking new feature of our formula for the entanglement entropy is the
appearance of a term scaling with the logarithm of the size of . This
logarithmic behaviour originates from certain discontinuities in the symbol of
the block Toeplitz matrix. Equipped with this formula we analyse the
entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev
fermionic chain with long range pairing.Comment: 27 pages, 5 figure
Elliptic Wess-Zumino-Witten Model from Elliptic Chern-Simons Theory
This letter continues the program aimed at analysis of the scalar product of
states in the Chern-Simons theory. It treats the elliptic case with group
SU(2). The formal scalar product is expressed as a multiple finite dimensional
integral which, if convergent for every state, provides the space of states
with a Hilbert space structure. The convergence is checked for states with a
single Wilson line where the integral expressions encode the Bethe-Ansatz
solutions of the Lame equation. In relation to the Wess-Zumino-Witten conformal
field theory, the scalar product renders unitary the
Knizhnik-Zamolodchikov-Bernard connection and gives a pairing between conformal
blocks used to obtain the genus one correlation functions.Comment: 18 pages, late
Dual branes in topological sigma models over Lie groups. BF-theory and non-factorizable Lie bialgebras
We complete the study of the Poisson-Sigma model over Poisson-Lie groups.
Firstly, we solve the models with targets and (the dual group of the
Poisson-Lie group ) corresponding to a triangular -matrix and show that
the model over is always equivalent to BF-theory. Then, given an
arbitrary -matrix, we address the problem of finding D-branes preserving the
duality between the models. We identify a broad class of dual branes which are
subgroups of and , but not necessarily Poisson-Lie subgroups. In
particular, they are not coisotropic submanifolds in the general case and what
is more, we show that by means of duality transformations one can go from
coisotropic to non-coisotropic branes. This fact makes clear that
non-coisotropic branes are natural boundary conditions for the Poisson-Sigma
model.Comment: 24 pages; JHEP style; Final versio
Reduction of Lie-Jordan algebras: Classical
In this paper we present a unified algebraic framework to discuss the reduction of classical and quantum systems. The underlying algebraic structure is a Lie-Jordan algebra supplemented, in the quantum case, with a Banach structure.
We discuss the reduction by symmetries, by constraints as well as the possible, non trivial, combinations of both. We finally introduce a new, general framework to perform the reduction of physical systems in an algebraic setup
Efficient formalism for large scale ab initio molecular dynamics based on time-dependent density functional theory
A new "on the fly" method to perform Born-Oppenheimer ab initio molecular
dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent
density functional theory, the electronic orbitals are evolved by a
Schroedinger-like equation, where the orbital time derivative is multiplied by
a parameter. This parameter controls the time scale of the fictitious
electronic motion and speeds up the calculations with respect to standard
Ehrenfest dynamics. In contrast to other methods, wave function orthogonality
needs not be imposed as it is automatically preserved, which is of paramount
relevance for large scale AIMD simulations.Comment: 5 pages, 3 color figures, revtex4 packag
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