Statistical Benchmarks for Quantum Transport in Complex Systems

Dimitri Kusnezov, Aurel Bulgac, Gui DoDang

Yan V. Fyodorov, Dmitry V. Savin

We review random matrix approaches to chaotic wave scattering and transport in open systems. Starting from the effective non-Hermitian Hamiltonian formulation, we discuss the scattering matrix, reaction matrix, time delays, and complex resonances as complementary probes of open chaotic dynamics. We emphasize universal statistics governed by symmetry, openness, and channel coupling. Topics include the maximum-entropy description of fixed-energy scattering and its applications to quantum transport, energy correlations, resonance and eigenfunction statistics, and selected wave-chaotic phenomena induced by finite absorption. The focus throughout is on non-perturbative methods and universal structures underlying open quantum and wave chaotic systems.

博 水田, hiroshi mizuta

Rudi Malfliet

Bohórquez Martínez, Oscar Hernando

In this work we study quantum transport phenomena in two different types of systems. The first type corresponds to so-called complex quantum systems, such as chaotic ballistic cavities and disordered quantum wires, which have a complex distribution of energy levels and transmission eigenvalues. This class of system does not admit a simple description in terms of a fixed Hamiltonian, and therefore we will make a statistical approach of its transport properties through Random Matrices Theory. We obtain exact expressions for the first three moments of the heat conductance of a quantum chain that crosses over from a superconducting quantum dot to a superconducting disordered quantum wire. Our analytic solution provides exact detailed descriptions of some smooth transitions that can be observed in the system as a function of its length, which include ballistic-metallic and metallic-insulating transitions. The two Bogolyubov de Gennes symmetry classes with time-reversal symmetry are accounted for. The striking effect of total suppression of the insulating regime in systems with broken spin-rotation invariance is observed at large length scales. For a single channel system, this anomalous effect can be interpreted as a signature of the presence of the elusive Majorana fermion in a condensed matter system. The second type of system corresponds to qubits, which, unlike complex systems, can be described by very simple Hamiltonians. In this case, we study the properties of open systems using master equations. We present a study of non-equilibrium thermodynamics of qubit systems submitted to quantum control. More specifically, we performed a comparative study of two types of simple two-level non-interacting quantum transport systems coupled to two bosonic and fermionic reservoirs respectively. Each system is submitted to a Wiseman-Milburn type feedback scheme in the formulation of stochastic thermodynamics. We see the effects of finite temperature and time delay on two specific feedback applications: a heat pump and a purification protocol. We observed a clear signature of the purity of the qubits in the Full Counting Statistics observed in the current flowing through the system.

Joel Linares, Boris Atenas, Sergio Curilef

Understanding wave-packet deformation and spreading is central to the description of transport and localization phenomena in both classical and quantum systems. In this work, we introduce information-theoretic and complexity-based indicators. We analyze the evolution of the probability distribution using Shannon and linear entropies, together with the inverse participation ratio, to quantify localization–delocalization processes and their associated fluctuations. These measures naturally motivate the use of statistical complexity definitions, including the López–Mancini–Calbet (CLMC) and Shiner–Davison–Landsberg (CSDL) complexities. In addition, we compute the probability current for both single-particle and two-particle configurations, providing a dynamical description of transport in terms of particle motion. The influence of an external field on entropy production, complexity, and probability currents is also examined, highlighting the interplay between information spreading, localization, and transport in lattice systems.