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M. Novaes

Publications and source records attributed to M. Novaes.

13 recordsLinked to original sources
arXiv2018

Time-inhomogeneous random Markov chains

We consider Markov chains with random transition probabilities which, moreover, fluctuate randomly with time. We describe such a system by a product of stochastic matrices, $U(t)=M_t\cdots M_1$, with the factors $M_i$ drawn independently from an ensemble of random Markov matrices, whose columns are independent Dirichlet random variables. The statistical properties of the columns of $U(t)$, its largest eigenvalue and its spectrum are obtained exactly for $N=2$ and numerically investigated for general $N$. For large $t$, the columns are Dirichlet-distributed, however the distribution is different from the initial one. As for the spectrum, we find that the eigenvalues converge to zero exponentially fast and investigate the statistics of the largest Lyapunov exponent, which is well approximated the a Gamma distribution. We also observe a concentration of the spectrum on the real line for large $t$.

math-ph↗
arXiv2011

Short periodic orbit approach to resonances and the fractal Weyl law

We investigate the properties of the semiclassical short periodic orbit approach for the study of open quantum maps that was recently introduced in [M. Novaes, J.M. Pedrosa, D. Wisniacki, G.G. Carlo, and J.P. Keating, Phys. Rev. E 80, 035202(R) 2009]. We provide conclusive numerical evidence, for the paradigmatic systems of the open baker and cat maps, that by using this approach the dimensionality of the eigenvalue problem is reduced according to the fractal Weyl law. The method also reproduces the projectors $|ψ^R_n><ψ_n^L|$, which involves the right and left states associated with a given eigenvalue and is supported on the classical phase space repeller.

quant-ph↗
arXiv2010

On inequivalent factorizations of a cycle

We introduce a bijection between inequivalent minimal factorizations of the n-cycle (1 2 ... n) into a product of smaller cycles of given length, on one side, and trees of a certain structure on the other. We use this bijection to count the factorizations with a given number of different commuting factors that can appear in the first and in the last positions, a problem which has found applications in physics. We also provide a necessary and sufficient condition for a set of cycles to be arrangeable into a product evaluating to (1 2 ... n).

math.CO↗
arXiv2009

Quantum chaotic resonances from short periodic orbits

We present an approach to calculating the quantum resonances and resonance wave functions of chaotic scattering systems, based on the construction of states localized on classical periodic orbits and adapted to the dynamics. Typically only a few of such states are necessary for constructing a resonance. Using only short orbits (with periods up to the Ehrenfest time), we obtain approximations to the longest living states, avoiding computation of the background of short living states. This makes our approach considerably more efficient than previous ones. The number of long lived states produced within our formulation is in agreement with the fractal Weyl law conjectured recently in this setting. We confirm the accuracy of the approximations using the open quantum baker map as an example.

nlin.CD↗
arXiv2008

On the resonance eigenstates of an open quantum baker map

We study the resonance eigenstates of a particular quantization of the open baker map. For any admissible value of Planck's constant, the corresponding quantum map is a subunitary matrix, and the nonzero component of its spectrum is contained inside an annulus in the complex plane, $|z_{min}|\leq |z|\leq |z_{max}|$. We consider semiclassical sequences of eigenstates, such that the moduli of their eigenvalues converge to a fixed radius $r$. We prove that, if the moduli converge to $r=|z_{max}|$, then the sequence of eigenstates converges to a fixed phase space measure $ρ_{max}$. The same holds for sequences with eigenvalue moduli converging to $|z_{min}|$, with a different limit measure $ρ_{min}$. Both these limiting measures are supported on fractal sets, which are trapped sets of the classical dynamics. For a general radius $|z_{min}|< r < |z_{max}|$, we identify families of eigenstates with precise self-similar properties.

nlin.CD↗
arXiv2008

Full counting statistics of chaotic cavities from classical action correlations

We present a trajectory-based semiclassical calculation of the full counting statistics of quantum transport through chaotic cavities, in the regime of many open channels. Our method to obtain the $m$th moment of the density of transmission eigenvalues requires two correlated sets of $m$ classical trajectories, therefore generalizing previous works on conductance and shot noise. The semiclassical results agree, for all values of $m$, with the corresponding predictions from random matrix theory.

cond-mat.mes-hall↗
arXiv2007

A model for chaotic dielectric microresonators

We develop a random-matrix model of two-dimensional dielectric resonators which combines internal wave chaos with the deterministic Fresnel laws for reflection and refraction at the interfaces. The model is used to investigate the statistics of the laser threshold and line width (lifetime and Petermann factor of the resonances) when the resonator is filled with an active medium. The laser threshold decreases for increasing refractive index $n$ and is smaller for TM polarization than for TE polarization, but is almost independent of the number of out-coupling modes $N$. The Petermann factor in the line width of the longest-living resonance also decreases for increasing $n$ and scales as $\sqrt{N}$, but is less sensitive to polarization. For resonances of intermediate lifetime, the Petermann factor scales linearly with $N$. These qualitative parametric dependencies are consistent with the random-matrix theory of resonators with small openings. However, for a small refractive index where the resonators are very open, the details of the statistics become non-universal. This is demonstrated by comparison with a particular dynamical model.

physics.optics↗
arXiv2006

Semiclassical structure of chaotic resonance eigenfunctions

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the non-unitary quantum propagator, and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as $\hbar\to 0$ on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates $\{ψ(\hbar)\}_{\hbar\to 0}$ is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker map, for which the probability density in position space is observed to have self-similarity properties.

quant-ph↗
arXiv2006

A new correlator in quantum spin chains

We propose a new correlator in one-dimensional quantum spin chains, the $s-$Emptiness Formation Probability ($s-$EFP). This is a natural generalization of the Emptiness Formation Probability (EFP), which is the probability that the first $n$ spins of the chain are all aligned downwards. In the $s-$EFP we let the spins in question be separated by $s$ sites. The usual EFP corresponds to the special case when $s=1$, and taking $s>1$ allows us to quantify non-local correlations. We express the $s-$EFP for the anisotropic XY model in a transverse magnetic field, a system with both critical and non-critical regimes, in terms of a Toeplitz determinant. For the isotropic XY model we find that the magnetic field induces an interesting length scale.

cond-mat.str-el↗
arXiv2006

Comb entanglement in quantum spin chains

Bipartite entanglement in the ground state of a chain of $N$ quantum spins can be quantified either by computing pairwise concurrence or by dividing the chain into two complementary subsystems. In the latter case the smaller subsystem is usually a single spin or a block of adjacent spins and the entanglement differentiates between critical and non-critical regimes. Here we extend this approach by considering a more general setting: our smaller subsystem $S_A$ consists of a {\it comb} of $L$ spins, spaced $p$ sites apart. Our results are thus not restricted to a simple `area law', but contain non-local information, parameterized by the spacing $p$. For the XX model we calculate the von-Neumann entropy analytically when $N\to \infty$ and investigate its dependence on $L$ and $p$. We find that an external magnetic field induces an unexpected length scale for entanglement in this case.

quant-ph↗
arXiv2005

Semiclassical propagation of spin coherent states

The semiclassical propagation of spin coherent states is considered in complex phase space. For two time-independent systems we find the appropriate classical trajectories and show that their combined contributions are able to describe quantum interference with great accuracy. Not only the modulus but also the phase of the quantum propagator, both dynamical and geometric terms combined, are accurately reproduced.

quant-ph↗
arXiv2005

Semiclassical propagation of coherent states using complex and real trajectories

We study the semiclassical propagation of coherent states in $d$ dimensions, which in general involves complex classical dynamics. Several simple approximations are derived that depend only on real classical trajectories, among them the thawed Gaussian approximation (TGA). Apart from the TGA, all other possibilities are able to reproduce interference and tunnelling effects, and involve propagating a set of classical initial conditions compatible with the quantum uncertainties. The accuracy of the results is verified in two dimensions for the scattering by an attractive potential, for a bound nonlinear system, for motion inside a circular billiard and for a system involving tunnelling.

quant-ph↗