arXiv subjects

Fabricio Toscano

Publications and source records attributed to Fabricio Toscano.

25 records · Page 2Linked to original sources

arXiv2008

WKB Propagation of Gaussian Wavepackets

We analyze the semiclassical evolution of Gaussian wavepackets in chaotic systems. We prove that after some short time a Gaussian wavepacket becomes a primitive WKB state. From then on, the state can be propagated using the standard TDWKB scheme. Complex trajectories are not necessary to account for the long-time propagation. The Wigner function of the evolving state develops the structure of a classical filament plus quantum oscillations, with phase and amplitude being determined by geometric properties of a classical manifold.

nlin.CD↗

arXiv2007

Husimi-Wigner representation of chaotic eigenstates

Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the cofactor Hilbert space. The collection of all the Wigner functions corresponding to a full set of parallel quantum sections defines the Husimi-Wigner reresentation. It occupies an intermediate ground between drastic suppression of nonclassical features, characteristic of Husimi functions, and the daunting complexity of higher dimensional Wigner functions. After analysing these features for simpler states, we exploit this new representation as a probe of numerically computed eigenstates of chaotic Hamiltonians. The individual two-dimensional Wigner functions resemble those of semiclassically quantized states, but the regular ring pattern is broken by dislocations.

nlin.CD↗

arXiv2006

Quantum to classical transition in a system with a mixed classical dynamics

We study how decoherence rules the quantum-classical transition of the Kicked Harmonic Oscillator (KHO). When the amplitude of the kick is changed the system presents a classical dynamics that range from regular to a strong chaotic behavior. We show that for regular and mixed classical dynamics, and in the presence of noise, the distance between the classical and the quantum phase space distributions is proportional to a single parameter $χ\equiv K\hbar_{\rm eff}^2/4D^{3/2}$ which relates the effective Planck constant $\hbar_{\rm eff}$, the kick amplitude $K$ and the diffusion constant $D$. This is valid when $χ< 1$, a case that is always attainable in the semiclassical regime independently of the value of the strength of noise given by $D$. Our results extend a recent study performed in the chaotic regime.

quant-ph↗

arXiv2004

Random matrix ensembles from nonextensive entropy

The classical Gaussian ensembles of random matrices can be constructed by maximizing Boltzmann-Gibbs-Shannon's entropy, S_{BGS} = - \int d{\bf H} [P({\bf H})] \ln [P({\bf H})], with suitable constraints. Here we construct and analyze random-matrix ensembles arising from the generalized entropy S_q = (1 - \int d{\bf H} [P({\bf H})]^q)/(q-1) (thus S_1=S_{BGS}). The resulting ensembles are characterized by a parameter q measuring the degree of nonextensivity of the entropic form. Making q -> 1 recovers the Gaussian ensembles. If q \ne 1, the joint probability distributions P(\bf H) cannot be factorized, i.e., the matrix elements of \bf H are correlated. In the limit of large matrices two different regimes are observed. When q<1, P(\bf H) has compact support, and the fluctuations tend asymptotically to those of the Gaussian ensembles. Anomalies appear for q>1: Both P(\bf H) and the marginal distributions P(H_{ij}) show power-law tails. Numerical analyses reveal that the nearest-neighbor spacing distribution is also long-tailed (not Wigner-Dyson) and, after proper scaling, very close to the result for the 2 x 2 case -- a generalization of Wigner's surmise. We discuss connections of these "nonextensive" ensembles with other non-Gaussian ones, like the so-called Lévy ensembles and those arising from soft-confinement.

cond-mat.stat-mech↗

arXiv2001

Semiclassical spatial correlations in chaotic wave functions

We study the spatial autocorrelation of energy eigenfunctions $ψ_n({\bf q})$ corresponding to classically chaotic systems in the semiclassical regime. Our analysis is based on the Weyl-Wigner formalism for the spectral average $C_ε({\bf q^{+}},{\bf q^{-}},E)$ of $ψ_n({\bf q}^{+})ψ_n^*({\bf q}^{-})$, defined as the average over eigenstates within an energy window $ε$ centered at $E$. In this framework $C_ε$ is the Fourier transform in momentum space of the spectral Wigner function $W({\bf x},E;ε)$. Our study reveals the chord structure that $C_ε$ inherits from the spectral Wigner function showing the interplay between the size of the spectral average window, and the spatial separation scale. We discuss under which conditions is it possible to define a local system independent regime for $C_ε$. In doing so, we derive an expression that bridges the existing formulae in the literature and find expressions for $C_ε({\bf q^{+}}, {\bf q^{-}},E)$ valid for any separation size $|{\bf q^{+}}-{\bf q^{-}}|$.

nlin.CD↗

arXiv2000

Scars of the Wigner function

We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical orbit of a Hamiltonian system with two degrees of freedom. The orbit is hyperbolic and the classical Hamiltonian is ``softly chaotic'' at the energies considered. The stationary wave functions are the familiar mixture of scarred and random waves, but the spectral average of the Wigner functions in part of the plane is nearly that of a harmonic oscillator and individual states are also remarkably regular. These results are interpreted in terms of the semiclassical picture of chords and centres, which leads to a qualitative explanation of the interference effects that are manifest in the other region of the plane. The qualitative picture is robust with respect to a canonical transformation that bends the orbit plane.

nlin.CD↗

arXiv1999

Geometrical approach to the distribution of the zeroes for the Husimi function

We construct a semiclassical expression for the Husimi function of autonomous systems in one degree of freedom, by smoothing with a Gaussian function an expression that captures the essential features of the Wigner function in the semiclassical limit. Our approximation reveals the "center and chord" estructure that the Husimi function inherits from the Wigner function, down to very shallow "valleys", where lie the Husimi zeroes. This explanation for the distribution of zeroes along curves relies on the geometry of the classical torus, rather than the complex analytical properties of the WKB method in the Bargmann representation. We evaluate the zeroes for several examples.

chao-dyn↗