Persistence of the spectral gap for the Landau–Pekar equations

AbstractThe Landau–Pekar equations describe the dynamics of a strongly coupled polaron. Here, we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for all times. For such initial data, this allows us to extend the results on the adiabatic theorem for the Landau–Pekar equations and their derivation from the Fröhlich model obtained in previous works to larger times.

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Strong Coupling and Nonextensive Thermodynamics

Entropy ◽

10.3390/e22090975 ◽

2020 ◽

Vol 22 (9) ◽

pp. 975

Author(s):

Rodrigo de Miguel ◽

J. Miguel Rubí

Keyword(s):

Thermodynamic Properties ◽

Effective Interaction ◽

Interaction Region ◽

Effective Hamiltonian ◽

Classical Concept ◽

Hamiltonian Approach ◽

Strongly Coupled ◽

Relative Term ◽

Nonextensive Thermodynamics ◽

Dividing Surface

We propose a Hamiltonian-based approach to the nonextensive thermodynamics of small systems, where small is a relative term comparing the size of the system to the size of the effective interaction region around it. We show that the effective Hamiltonian approach gives easy accessibility to the thermodynamic properties of systems strongly coupled to their surroundings. The theory does not rely on the classical concept of dividing surface to characterize the system’s interaction with the environment. Instead, it defines an effective interaction region over which a system exchanges extensive quantities with its surroundings, easily producing laws recently shown to be valid at the nanoscale.

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EQUATION OF STATE OF STRONGLY COUPLED HAMILTONIAN LATTICE QCD AT FINITE DENSITY

Modern Physics Letters A ◽

10.1142/s0217732302009234 ◽

2002 ◽

Vol 17 (38) ◽

pp. 2513-2521 ◽

Cited By ~ 2

Author(s):

YASUO UMINO

Keyword(s):

Equation Of State ◽

Lattice Qcd ◽

Mean Field ◽

Equation Of Motion ◽

Continuum Models ◽

Effective Hamiltonian ◽

Mechanical Instability ◽

Finite Density ◽

Strongly Coupled ◽

Hamiltonian Lattice

We calculate the equation of state of strongly coupled Hamiltonian lattice QCD at finite density by constructing a solution to the equation of motion corresponding to an effective Hamiltonian describing the ground state of the theory with Wilson fermions. To lowest order in N c we find that the pressure of the quark Fermi sea can be negative indicating its mechanical instability. This new mean field result is in qualitative agreement with continuum models and should be verifiable by future numerical simulations.

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Robust Diabatic Grover Search by Landau–Zener–Stückelberg Oscillations

Entropy ◽

10.3390/e21100937 ◽

2019 ◽

Vol 21 (10) ◽

pp. 937

Author(s):

Yosi Atia ◽

Yonathan Oren ◽

Nadav Katz

Keyword(s):

Quantum Computation ◽

Ground State ◽

Spectral Gap ◽

Quantum Circuit ◽

Computational Time ◽

Adiabatic Theorem ◽

Grover Algorithm ◽

Oscillation Phenomenon ◽

Two Level Systems ◽

Grover Search

Quantum computation by the adiabatic theorem requires a slowly-varying Hamiltonian with respect to the spectral gap. We show that the Landau–Zener–Stückelberg oscillation phenomenon, which naturally occurs in quantum two-level systems under non-adiabatic periodic drive, can be exploited to find the ground state of an N-dimensional Grover Hamiltonian. The total runtime of this method is O ( 2 n ) , which is equal to the computational time of the Grover algorithm in the quantum circuit model. An additional periodic drive can suppress a large subset of Hamiltonian control errors by using coherent destruction of tunneling, thus outperforming previous algorithms.

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Remarks on nonlinear elastic waves with null conditions

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2020039 ◽

2020 ◽

Vol 26 ◽

pp. 121

Author(s):

Dongbing Zha ◽

Weimin Peng

Keyword(s):

Initial Data ◽

Global Existence ◽

Elastic Waves ◽

Wave Equations ◽

Alternative Proof ◽

Classical Solutions ◽

Small Initial Data ◽

Hyperelastic Materials ◽

Variational Structure ◽

Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

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