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Superconducting Contacts beyond the Tunneling Limit
Published in Andrei D. Zaikin, Dmitry S. Golubev, Dissipative Quantum Mechanics of Nanostructures, 2019
Andrei D. Zaikin, Dmitry S. Golubev
For smaller values of C, the plasma frequency becomes higher, and one can even reach the limit ωJ(0) > ωmax in which case damping due to quasiparticles above the gap sets in. With increasing I, the plasma frequency decreases, first reaching the value ωJ(χ1) = ωmax (17.105) at a phase value χ = χ1 and then approaching ωmin at χ = χ2 > χ1. Within this scenario, quasiparticles are responsible for dissipation for 0 < I < IS(χ1), while at higher bias values IS(χ1) < I < IS(χ2), quantum dissipation is solely due to Andreev levels. At even bigger currents I > IS(χ2), no dissipation occurs, and the capacitance renormalization (17.41) remains the only effect of the environment.
Adaptive Quantum Monte Carlo Approach States for High-Dimensional Systems
Published in Xavier Oriols, Jordi Mompart, Applied Bohmian Mechanics, 2019
Eric R. Bittner, Donald J. Kouri, Sean Derrickson, Jeremy B. Maddox
Numerical solutions of the time-dependent Schrödinger equation are traditionally obtained by calculating the short-time quantum propagator using fast Fourier transforms [69], finite basis sets, or discrete variable representations [73]. Typically, the computational overhead associated with these techniques scales exponentially with the dimensionality of the physical problem. Trajectory-based methodologies, on the other hand, offer tremendous numerical scaling advantages, especially for high-dimensional systems where traditional techniques are not feasible. In particular, the Bohm interpretation of QM has inspired a growing number of theoretical and computational studies involving a wide range of problems such as reactive scattering dynamics [95, 107], tunneling systems [11, 12, 77, 92], mixed quantum/classical simulations [46–48, 91], electronic transitions [20, 108, 109], photodissociation [38, 53, 85, 103], mixed quantum states [21, 22], and quantum dissipation [80, 81, 110].
Statistical quasi-particle theory for open quantum systems
Published in Molecular Physics, 2018
Hou-Dao Zhang, Rui-Xue Xu, Xiao Zheng, YiJing Yan
As a non-perturbative and non-Markovian quantum dissipation theory, DEOM is often numerically expensive. The major challenge of this approach is the rapidly increasing memory space for storing and computing those DDOs in the hierarchy. Therefore, reducing the number of DDOs will dramatically enhance the efficiency. We tackle this problem from the optimal DEOM formalism construction aspect, via developing minimal basis-set dissipaton decomposition and efficient hierarchy truncation schemes. In addition, we propose some advancing numerical methods, which promote the DEOM approach to be an efficient dynamical propagator and steady-state solver for open system questions.
Spontaneous emission from nonhermitian perspective: complex scaling of the photon coordinates
Published in Molecular Physics, 2019
It is well known that SE plays a crucial role in numerous basic phenomena of atomic, molecular and optical (AMOP) physics [5]. Namely in different fields of spectroscopy [6], in quantum optics [7,8], in the theory of lasers [9], or e.g. in laser cooling and trapping of cold atoms [5,10]. Theoretical description of SE for the just listed examples is almost exclusively based upon the quantum dissipation formalism [5,11,12]. These approaches lead towards an approximative (non)Markovian master equation for the reduced density operator of the atomic/molecular system, or even to a formally exact hierarchy of master type equations of increasing complexity (see e.g. Ref. [13]).