scholarly journals The Lieb–Thirring Inequality for Interacting Systems in Strong-Coupling Limit

2021 ◽  
Author(s):  
Kevin Kögler ◽  
Phan Thành Nam
Keyword(s):  
Strong Coupling ◽  
Quantum Systems ◽  
Interpolation Inequality ◽  
Wave Functions ◽  
Strong Coupling Limit ◽  
Repulsive Interaction ◽  
Interaction Potentials ◽  
Optimal Constant ◽  
Interacting Systems ◽  
The One

AbstractWe consider an analogue of the Lieb–Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show that in the strong-coupling limit, the Lieb–Thirring constant converges to the optimal constant of the one-body Gagliardo–Nirenberg interpolation inequality without interaction.

scholarly journals Fundamental limitations of the mode temperature concept in strongly coupled systems

2020 ◽  
Vol 75 (8) ◽  
pp. 803-807
Author(s):  
Svend-Age Biehs ◽  
Achim Kittel ◽  
Philippe Ben-Abdallah
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Strong Coupling ◽  
Quantum Systems ◽  
Coupled Systems ◽  
Strong Coupling Limit ◽  
Strongly Coupled ◽  
Fundamental Limitations ◽  
Temperature Concept ◽  
Vacuum Gap

AbstractWe theoretically analyze heat exchange between two quantum systems in interaction with external thermostats. We show that in the strong coupling limit the widely used concept of mode temperatures loses its thermodynamic foundation and therefore cannot be employed to make a valid statement on cooling and heating in such systems; instead, the incorrectly applied concept may result in a severe misinterpretation of the underlying physics. We illustrate these general conclusions by discussing recent experimental results reported on the nanoscale heat transfer through quantum fluctuations between two nanomechanical membranes separated by a vacuum gap.

scholarly journals Temperature correlators in the one-dimensional Hubbard model in the strong coupling limit

1998 ◽  
Vol 245 (6) ◽  
pp. 537-547 ◽  
Author(s):  
A.G Izergin ◽  
A.G Pronko ◽  
N.I Abarenkova
Keyword(s):  
Hubbard Model ◽  
Strong Coupling ◽  
Strong Coupling Limit ◽  
One Dimensional ◽  
The One

STRONG COUPLING APPROACH TO ONE-DIMENSIONAL HUBBARD MODEL AND RELATED LATTICE MODELS

1999 ◽  
Vol 13 (05n06) ◽  
pp. 731-740 ◽  
Author(s):  
H. SHIBA ◽  
K. PENC ◽  
F. MILA
Keyword(s):  
Hubbard Model ◽  
Strong Coupling ◽  
Lattice Models ◽  
Wave Functions ◽  
Spectral Functions ◽  
Spin Part ◽  
One Dimensional ◽  
Coupling Approach ◽  
The One ◽  
Charge Part

The strong coupling limit of one-dimensional correlated systems is nontrivial, but simple in some sense. Here we demonstrate it, discussing the wave functions for the 1D U→ +∞ Hubbard model, which are factorized as a direct product of the charge part and the spin part and determining the one-particle spectral functions explicitly.

THE SPINLESS FALICOV–KIMBALL MODEL AWAY FROM HALF-FILLING

1999 ◽  
Vol 13 (15) ◽  
pp. 515-522 ◽  
Author(s):  
ŠTEFAN GÁL
Keyword(s):  
Strong Coupling ◽  
Ground State ◽  
Low Temperatures ◽  
Exact Diagonalization ◽  
Strong Coupling Limit ◽  
Small Cluster ◽  
One Dimensional ◽  
Small Band ◽  
Half Filling ◽  
The One

The one-dimensional spinless Falicov–Kimball (FKM) model is studied in the strong coupling limit away from half-filling. The small-cluster exact-diagonalization calculations are employed to obtain valence transitions in the ground state and for finite temperatures. It is found that in the ground state, the model describes continuous valence transitions for small band-fillings and both continuous and discontinuous transitions near half-filling. At finite temperatures, only continuous valence transitions are obtained. The valence is integer at low temperatures for small band-fillings and in other cases, it takes only intermediate values.

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