scholarly journals Ground state of nonassociative hydrogen and upper bounds on the magnetic charge of elementary particles

2021 ◽  
Vol 104 (10) ◽  
Author(s):  
Martin Bojowald ◽  
Suddhasattwa Brahma ◽  
Umut Büyükçam ◽  
Martijn van Kuppeveld
Keyword(s):  
Ground State ◽  
Magnetic Charge ◽  
Upper Bounds ◽  
Elementary Particles

scholarly journals Target space entanglement in quantum mechanics of fermions and matrices

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Sotaro Sugishita
Keyword(s):  
Mutual Information ◽  
Ground State ◽  
Entanglement Entropy ◽  
Algebraic Approach ◽  
Upper Bounds ◽  
Wave Functions ◽  
Target Space ◽  
Single Interval ◽  
Area Law ◽  
Formula Expression

Abstract We consider entanglement of first-quantized identical particles by adopting an algebraic approach. In particular, we investigate fermions whose wave functions are given by the Slater determinants, as for singlet sectors of one-matrix models. We show that the upper bounds of the general Rényi entropies are N log 2 for N particles or an N × N matrix. We compute the target space entanglement entropy and the mutual information in a free one-matrix model. We confirm the area law: the single-interval entropy for the ground state scales as $$ \frac{1}{3} $$ 1 3 log N in the large N model. We obtain an analytical $$ \mathcal{O}\left({N}^0\right) $$ O N 0 expression of the mutual information for two intervals in the large N expansion.

UNIFORM UPPER BOUNDS IN THE FRÖHLICH POLARON THEORY

1993 ◽  
Vol 07 (27) ◽  
pp. 1773-1779 ◽  
Author(s):  
N.N. BOGOLUBOV ◽  
A.V. SOLDATOV
Keyword(s):  
Interaction Parameter ◽  
Ground State Energy ◽  
Upper Bound ◽  
Ground State ◽  
State Energy ◽  
Upper Bounds ◽  
Simple Method ◽  
Polaron Theory

We present a very simple method to derive the upper bound of the ground-state energy for the Fröhlich polaron theory. The obtained bounds are proved to be uniform for all values of the interaction parameter.

VARIATIONAL APPROACH TO POLARON PROBLEM

1987 ◽  
Vol 01 (01) ◽  
pp. 89-102 ◽  
Author(s):  
N.N. BOGOLUBOV ◽  
A.N. KIREEV ◽  
A.M. KURBATOV
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
Variational Approach ◽  
State Energy ◽  
Interaction Strength ◽  
Upper Bounds ◽  
Minimal Solution ◽  
Strong Interactions ◽  
Simple Models

Variational Ansatz to describe the ground state of Fröhlich’s Polaron at all interaction strength is proposed. The best upper bounds to the polaron ground state energy are obtained in the limiting cases of weak and strong interactions. For intermediate couplings two simple models are investigated. The ground state energy does not exceed their minimal solution.

GENERALIZED VARIATIONAL PRINCIPLE IN QUANTUM MECHANICS

1995 ◽  
Vol 09 (22) ◽  
pp. 2899-2936 ◽  
Author(s):  
A.V. SOLDATOV
Keyword(s):  
Quantum Mechanics ◽  
Variational Principle ◽  
Quantum System ◽  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Convergent Sequence ◽  
Upper Bounds ◽  
Generalized Variational Principle ◽  
Quantitative Characteristics

An algorithm is proposed that allows us to derive the convergent sequence of upper bounds for the ground state energy of a quantum system. The algorithm generalizes the well-known variational principle of quantum mechanics and moreover provides qualitative, and under some additional conditions even quantitative, characteristics of the spectrum of a quantum system as a whole.

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