Numerical linked cluster expansions for inhomogeneous systems

This chapter contains the essential statistical mechanics required to understand the inner workings of, and interpretation of results from, computer simulations. The microcanonical, canonical, isothermal–isobaric, semigrand and grand canonical ensembles are defined. Thermodynamic, structural, and dynamical properties of simple and complex liquids are related to appropriate functions of molecular positions and velocities. A number of important thermodynamic properties are defined in terms of fluctuations in these ensembles. The effect of the inclusion of hard constraints in the underlying potential model on the calculated properties is considered, and the addition of long-range and quantum corrections to classical simulations is presented. The extension of statistical mechanics to describe inhomogeneous systems such as the planar gas–liquid interface, fluid membranes, and liquid crystals, and its application in the simulation of these systems, are discussed.

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Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators

Mathematical Physics Analysis and Geometry ◽

10.1007/s11040-021-09375-5 ◽

2021 ◽

Vol 24 (1) ◽

Author(s):

Luca Fresta

Keyword(s):

Density Of States ◽

Local Density ◽

Schrödinger Operators ◽

Random Schrödinger Operators ◽

Schrodinger Operators ◽

Local Density Of States ◽

Weak Disorder ◽

Cluster Expansions ◽

Strong Disorder ◽

Lifshitz Tail

AbstractWe study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.

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Quantum Conductivity of Spatially Inhomogeneous Systems

MRS Proceedings ◽

10.1557/proc-789-n3.10 ◽

2003 ◽

Vol 789 ◽

Cited By ~ 2

Author(s):

Liudmila A. Pozhar

Keyword(s):

Charge Density ◽

Evolution Equations ◽

Original Method ◽

Theoretical Description ◽

Inhomogeneous System ◽

Inhomogeneous Systems ◽

Spatially Inhomogeneous ◽

Significant Step ◽

Quantum Current ◽

Electro Magnetic

ABSTRACTA fundamental quantum theory of conductivity of spatially inhomogeneous systems in weak electro-magnetic fields has been derived using a two-time Green function (TTGF)-based technique that generalizes the original method due to Zubarev and Tserkovnikov (ZT). Quantum current and charge density evolution equations are derived in a linear approximation with regard to the field potentials. Explicit expressions for the longitudinal and transverse conductivity, and dielectric and magnetic susceptibilities have been derived in terms of charge density - charge density and microcurrent - microcurrent TTGFs. The obtained theoretical description and formulae are applicable to any inhomogeneous system, such as artificial molecules, atomic and molecular clusters, thin films, interfacial systems, etc. In particular, the theory is designed to predict charge transport properties of small semiconductor quantum dots (QDs) and wells (QWs), and is a significant step toward realization of a concept of virtual (i.e., theory-based, computational) synthesis of electronic nanomaterials of prescribed electronic properties.

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