Quantum Versus Classical Decay Laws in Open Chaotic Systems

We study analytically the time evolution in decaying chaotic systems and discuss in detail the hierarchy of characteristic time scales that appeared in the quasiclassical region. There exist two quantum time scales: the Heisenberg time t_H and the time t_q=t_H/\sqrt{\kappa T} (with \kappa >> 1 and T being the degree of resonance overlapping and the transmission coefficient respectively) associated with the decay. If t_q < t_H the quantum deviation from the classical decay law starts at the time t_q and are due to the openness of the system. Under the opposite condition quantum effects in intrinsic evolution begin to influence the decay at the time t_H. In this case we establish the connection between quantities which describe the time evolution in an open system and their closed counterparts.Comment: 3 pages, REVTeX, no figures, replaced with the published version (misprints corrected, references updated

Statistics of resonance width shifts as a signature of eigenfunction non-orthogonality

We consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the non-orthogonality of resonance wavefunctions, being zero only if those were orthogonal. Focusing further on chaotic systems, we employ random matrix theory to introduce a new type of parametric statistics in open systems, and derive the distribution of the resonance width shifts in the regime of weak coupling to the continuum.Comment: 4 pages, 1 figure (published version with minor changes

Statistics of eigenfunctions in open chaotic systems: a perturbative approach

We investigate the statistical properties of the complexness parameter which characterizes uniquely complexness (biorthogonality) of resonance eigenstates of open chaotic systems. Specifying to the regime of isolated resonances, we apply the random matrix theory to the effective Hamiltonian formalism and derive analytically the probability distribution of the complexness parameter for two statistical ensembles describing the systems invariant under time reversal. For those with rigid spectra, we consider a Hamiltonian characterized by a picket-fence spectrum without spectral fluctuations. Then, in the more realistic case of a Hamiltonian described by the Gaussian Orthogonal Ensemble, we reveal and discuss the r\^ole of spectral fluctuations

Efficient semiclassical approach for time delays

The Wigner time delay, defined by the energy derivative of the total scattering phase shift, is an important spectral measure of an open quantum system characterizing the duration of the scattering event. It is proportional to the trace of the Wigner-Smith matrix Q that also encodes other time-delay characteristics. For chaotic cavities, these quantities exhibit universal fluctuations that are commonly described within random matrix theory. Here, we develop a new semiclassical approach to the time-delay matrix which is formulated in terms of the classical trajectories that connect the exterior and interior regions of the system. This approach is superior to previous treatments because it avoids the energy derivative. We demonstrate the method's efficiency by going beyond previous work in establishing the universality of time-delay statistics for chaotic cavities with perfectly connected leads. In particular, the moment generating function of the proper time-delays (eigenvalues of Q) is found semiclassically for the first five orders in the inverse number of scattering channels for systems with and without time-reversal symmetry. We also show the equivalence of random matrix and semiclassical results for the second moments and for the variance of the Wigner time delay at any channel number.https://arxiv.org/abs/1409.1532v

Distribution of reflection eigenvalues in many-channel chaotic cavities with absorption

The reflection matrix R=S^{\dagger}S, with S being the scattering matrix, differs from the unit one, when absorption is finite. Using the random matrix approach, we calculate analytically the distribution function of its eigenvalues in the limit of a large number of propagating modes in the leads attached to a chaotic cavity. The obtained result is independent on the presence of time-reversal symmetry in the system, being valid at finite absorption and arbitrary openness of the system. The particular cases of perfectly and weakly open cavities are considered in detail. An application of our results to the problem of thermal emission from random media is briefly discussed.Comment: 4 pages, 2 figures; (Ref.[5b] added, appropriate modification in text

Delay times and reflection in chaotic cavities with absorption

Absorption yields an additional exponential decay in open quantum systems which can be described by shifting the (scattering) energy E along the imaginary axis, E+i\hbar/2\tau_{a}. Using the random matrix approach, we calculate analytically the distribution of proper delay times (eigenvalues of the time-delay matrix) in chaotic systems with broken time-reversal symmetry that is valid for an arbitrary number of generally nonequivalent channels and an arbitrary absorption rate 1/\tau_{a}. The relation between the average delay time and the ``norm-leakage'' decay function is found. Fluctuations above the average at large values of delay times are strongly suppressed by absorption. The relation of the time-delay matrix to the reflection matrix S^{\dagger}S is established at arbitrary absorption that gives us the distribution of reflection eigenvalues. The particular case of single-channel scattering is explicitly considered in detail.Comment: 5 pages, 3 figures; final version to appear in PRE (relation to reflection extended, new material with Fig.3 added, experiment cond-mat/0305090 discussed

Reducing nonideal to ideal coupling in random matrix description of chaotic scattering: Application to the time-delay problem

We write explicitly a transformation of the scattering phases reducing the problem of quantum chaotic scattering for systems with M statistically equivalent channels at nonideal coupling to that for ideal coupling. Unfolding the phases by their local density leads to universality of their local fluctuations for large M. A relation between the partial time delays and diagonal matrix elements of the Wigner-Smith matrix is revealed for ideal coupling. This helped us in deriving the joint probability distribution of partial time delays and the distribution of the Wigner time delay.Comment: 4 pages, revtex, no figures; published versio

Wigner-Smith time-delay matrix in chaotic cavities with non-ideal contacts

We consider wave propagation in a complex structure coupled to a finite number N of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the concept of time delays, relatedtotheenergy(orfrequency)derivativeofthescatteringmatrixS. Wedeveloparandom matrixapproachtostudythestatisticalpropertiesofthesymmetrisedWigner-Smithtime-delay matrix Qs = −i~S−1/2∂εS S−1/2, and obtain the joint distribution of S and Qs for the systemwithnon-idealcontacts,characterisedbyafinitetransmissionprobability(perchannel) 0 < T 6 1. WederivetworepresentationsofthedistributionofQs intermsofmatrixintegrals specified by the Dyson symmetry index β = 1, 2, 4 (the general case of unequally coupled channels is also discussed). We apply this to the Wigner time delay τW = (1/N)tr Qs , which is an important quantity providing the density of states of the open system. Using the obtainedresults,wedeterminethedistribution PN,β(τ) oftheWignertimedelayintheweak coupling limit NT 1 and identify the following three regimes. (i) The large deviations at small times (measured in units of the Heisenberg time) are characterised by the limiting behaviour PN,β(τ) ∼ τ−βN2/2−3/2 exp −βNT/(8τ) for τ . T. (ii) The distribution shows the universal τ−3/2 behaviour in some intermediate range T . τ . 1/(TN2). (iii) It has a power law decay PN,β(τ) ∼ T2N3(TN2τ)−2−βN/2 for large τ & 1/(TN2)

Recommended reading list of early publications on atomic layer deposition-Outcome of the "Virtual Project on the History of ALD"

Atomic layer deposition (ALD), a gas-phase thin film deposition technique based on repeated, self-terminating gas-solid reactions, has become the method of choice in semiconductor manufacturing and many other technological areas for depositing thin conformal inorganic material layers for various applications. ALD has been discovered and developed independently, at least twice, under different names: atomic layer epitaxy (ALE) and molecular layering. ALE, dating back to 1974 in Finland, has been commonly known as the origin of ALD, while work done since the 1960s in the Soviet Union under the name "molecular layering" (and sometimes other names) has remained much less known. The virtual project on the history of ALD (VPHA) is a volunteer-based effort with open participation, set up to make the early days of ALD more transparent. In VPHA, started in July 2013, the target is to list, read and comment on all early ALD academic and patent literature up to 1986. VPHA has resulted in two essays and several presentations at international conferences. This paper, based on a poster presentation at the 16th International Conference on Atomic Layer Deposition in Dublin, Ireland, 2016, presents a recommended reading list of early ALD publications, created collectively by the VPHA participants through voting. The list contains 22 publications from Finland, Japan, Soviet Union, United Kingdom, and United States. Up to now, a balanced overview regarding the early history of ALD has been missing; the current list is an attempt to remedy this deficiency. (C) 2016 Author(s).Peer reviewe