538,521 research outputs found
Quantum theta functions and Gabor frames for modulation spaces
Representations of the celebrated Heisenberg commutation relations in quantum
mechanics and their exponentiated versions form the starting point for a number
of basic constructions, both in mathematics and mathematical physics (geometric
quantization, quantum tori, classical and quantum theta functions) and signal
analysis (Gabor analysis).
In this paper we try to bridge the two communities, represented by the two
co--authors: that of noncommutative geometry and that of signal analysis. After
providing a brief comparative dictionary of the two languages, we will show
e.g. that the Janssen representation of Gabor frames with generalized Gaussians
as Gabor atoms yields in a natural way quantum theta functions, and that the
Rieffel scalar product and associativity relations underlie both the functional
equations for quantum thetas and the Fundamental Identity of Gabor analysis.Comment: 38 pages, typos corrected, MSC class change
Dynamical correlations and quantum phase transition in the quantum Potts model
We present a detailed study of the finite temperature dynamical properties of
the quantum Potts model in one dimension.Quasiparticle excitations in this
model have internal quantum numbers, and their scattering matrix {\gf deep} in
the gapped phases is shown to take a simple {\gf exchange} form in the
perturbative regimes. The finite temperature correlation functions in the
quantum critical regime are determined using conformal invariance, while {\gf
far from the quantum critical point} we compute the decay functions
analytically within a semiclassical approach of Sachdev and Damle [K. Damle and
S. Sachdev, Phys. Rev. B \textbf{57}, 8307 (1998)]. As a consequence, decay
functions exhibit a {\em diffusive character}. {\gf We also provide robust
arguments that our semiclassical analysis carries over to very low temperatures
even in the vicinity of the quantum phase transition.} Our results are also
relevant for quantum rotor models, antiferromagnetic chains, and some spin
ladder systems.Comment: 18 PRB pages added correction
Scale invariant distribution functions in quantum systems with few degrees of freedom
Scale invariance usually occurs in extended systems where correlation
functions decay algebraically in space and/or time. Here we introduce a new
type of scale invariance, occurring in the distribution functions of physical
observables. At equilibrium these functions decay over a typical scale set by
the temperature, but they can become scale invariant in a sudden quantum
quench. We exemplify this effect through the analysis of linear and non-linear
quantum oscillators. We find that their distribution functions generically
diverge logarithmically close to the stable points of the classical dynamics.
Our study opens the possibility to address integrability and its breaking in
distribution functions, with immediate applications to matter-wave
interferometers.Comment: 8+10 pages. Scipost Submissio
Scale invariant distribution functions in quantum systems with few degrees of freedom
Scale invariance usually occurs in extended systems where correlation
functions decay algebraically in space and/or time. Here we introduce a new
type of scale invariance, occurring in the distribution functions of physical
observables. At equilibrium these functions decay over a typical scale set by
the temperature, but they can become scale invariant in a sudden quantum
quench. We exemplify this effect through the analysis of linear and non-linear
quantum oscillators. We find that their distribution functions generically
diverge logarithmically close to the stable points of the classical dynamics.
Our study opens the possibility to address integrability and its breaking in
distribution functions, with immediate applications to matter-wave
interferometers.Comment: 8+10 pages. Scipost Submissio
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