4,179 research outputs found
Quantum-to-Classical Correspondence and Hubbard-Stratonovich Dynamical Systems, a Lie-Algebraic Approach
We propose a Lie-algebraic duality approach to analyze non-equilibrium
evolution of closed dynamical systems and thermodynamics of interacting quantum
lattice models (formulated in terms of Hubbard-Stratonovich dynamical systems).
The first part of the paper utilizes a geometric Hilbert-space-invariant
formulation of unitary time-evolution, where a quantum Hamiltonian is viewed as
a trajectory in an abstract Lie algebra, while the sought-after evolution
operator is a trajectory in a dynamic group, generated by the algebra via
exponentiation. The evolution operator is uniquely determined by the
time-dependent dual generators that satisfy a system of differential equations,
dubbed here dual Schrodinger-Bloch equations, which represent a viable
alternative to the conventional Schrodinger formulation. These dual
Schrodinger-Bloch equations are derived and analyzed on a number of specific
examples. It is shown that deterministic dynamics of a closed classical
dynamical system occurs as action of a symmetry group on a classical manifold
and is driven by the same dual generators as in the corresponding quantum
problem. This represents quantum-to-classical correspondence. In the second
part of the paper, we further extend the Lie algebraic approach to a wide class
of interacting many-particle lattice models. A generalized Hubbard-Stratonovich
transform is proposed and it is used to show that the thermodynamic partition
function of a generic many-body quantum lattice model can be expressed in terms
of traces of single-particle evolution operators governed by the dynamic
Hubbard-Stratonovich fields. Finally, we derive Hubbard-Stratonovich dynamical
systems for the Bose-Hubbard model and a quantum spin model and use the
Lie-algebraic approach to obtain new non-perturbative dual descriptions of
these theories.Comment: 25 pages, 1 figure; v2: citations adde
Dangerous implications of a minimum length in quantum gravity
The existence of a minimum length and a generalization of the Heisenberg
uncertainty principle seem to be two fundamental ingredients required in any
consistent theory of quantum gravity. In this letter we show that they would
predict dangerous processes which are phenomenologically unacceptable. For
example, long--lived virtual super--Planck mass black holes may lead to rapid
proton decay. Possible solutions of this puzzle are briefly discussed.Comment: 5 pages, no figure. v3: refereed versio
Extremal states for photon number and quadratures as gauges for nonclassicality
Rotated quadratures carry the phase-dependent information of the
electromagnetic field, so they are somehow conjugate to the photon number. We
analyze this noncanonical pair, finding an exact uncertatinty relation, as well
as a couple of weaker inequalities obtained by relaxing some restrictions of
the problem. We also find the intelligent states saturating that relation and
complete their characterization by considering extra constraints on the
second-order moments of the variables involved. Using these moments, we
construct performance measures tailored to diagnose photon-added and
Schr\"odinger catlike states, among others.Comment: 6 pages, 4 color figures. Comments welcome
How to decompose arbitrary continuous-variable quantum operations
We present a general, systematic, and efficient method for decomposing any
given exponential operator of bosonic mode operators, describing an arbitrary
multi-mode Hamiltonian evolution, into a set of universal unitary gates.
Although our approach is mainly oriented towards continuous-variable quantum
computation, it may be used more generally whenever quantum states are to be
transformed deterministically, e.g. in quantum control, discrete-variable
quantum computation, or Hamiltonian simulation. We illustrate our scheme by
presenting decompositions for various nonlinear Hamiltonians including quartic
Kerr interactions. Finally, we conclude with two potential experiments
utilizing offline-prepared optical cubic states and homodyne detections, in
which quantum information is processed optically or in an atomic memory using
quadratic light-atom interactions.Comment: Ver. 3: published version with supplementary materia
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