Grüneisen parameters for the Lieb-Liniger and Yang-Gaudin models

Li, Peng; Yu, Yifei; Guan, Xi-Wen

doi:10.1103/physrevb.100.245435

Cited by 10 publications

(11 citation statements)

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“…For a three-dimensional free gas [40], it is clear that mag = int = 0 and thus = 2/d. A further study of the identity (13) will be published elsewhere [41].…”

Section: An Exact Identitymentioning

confidence: 99%

“…In the above equation, n is the density, G(x) is the scaling function, and μ is an effective chemical potential [24]. A more detailed study on the quantum scalings of the GPs (17) was published elsewhere [41]. In addition, the use of magnetic and interacting GPs (9) and (11) also gives the same phase diagram at low temperatures.…”

Section: Hamiltonian Of the Yang-gaudin Modelmentioning

confidence: 99%

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Grüneisen parameters: Origin, identity, and quantum refrigeration

Zhang²,

Guan

2020

Phys. Rev. Research

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In solid-state physics, the Grüneisen parameter (GP) was first introduced to study the effect of volume change of a crystal lattice on its vibrational frequencies and has since been widely used to investigate the characteristic energy scales of systems associated with the changes of external potentials. However, the GP is less investigated in gas systems and especially strongly interacting quantum gases. Here we report on some general results on the origin of the GP, an identity, and caloric effects in ultracold quantum gases. We prove that there exists a simple identity among three different types of GPs, quantifying the caloric effect induced by variations of volume, magnetic field, and interaction, respectively. Using exact Bethe ansatz solutions, we present a rigorous study of these different GPs and the quantum refrigeration in one-dimensional Bose and Fermi gases. Based on the exact equations of states of these systems, we further obtain analytic results for singular behavior of the GPs and the caloric effects at quantum criticality. We also predict the existence of the lowest temperature for cooling near a quantum phase transition. It turns out that the interaction ramp up and down in quantum gases provide a promising protocol of quantum refrigeration in addition to the usual adiabatic demagnetization cooling in solid-state materials.

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“…For a three-dimensional free gas [40], it is clear that mag = int = 0 and thus = 2/d. A further study of the identity (13) will be published elsewhere [41].…”

Section: An Exact Identitymentioning

confidence: 99%

Section: Hamiltonian Of the Yang-gaudin Modelmentioning

confidence: 99%

Grüneisen parameters: Origin, identity, and quantum refrigeration

Zhang²,

Guan

2020

Phys. Rev. Research

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“…from which all the thermal and magnetic quantities, as well as other relevant physical properties, such as Wilson ratio [123] and Grüneisen parameter [124,125], can be derived according to the standard statistical relations. For a attractive interaction, i.e.…”

Section: Yang-gaudin Modelmentioning

confidence: 99%

New trends in quantum integrability: Recent experiments with ultracold atoms

Guan¹,

He²

2022

Preprint

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Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang-Baxter systems have been successfully realized allowing us to confront elegant and sophisticated exact solutions of these systems with their experimental counterparts. The new experimental developments show a variety of fundamental one-dimensional (1D) phenomena, ranging from the generalized hydrodynamics to dynamical fermionization, Tomonaga-Luttinger liquids, collective excitations, fractional exclusion statistics, quantum holonomy, spin-charge separation, competing orders with high spin symmetry and quantum impurity problems. This article briefly reviews these developments and provides rigorous understanding of those observed phenomena based on the exact solutions while highlighting the uniqueness of 1D quantum physics. The precision of atomic physics realizations of integrable many-body problems continues to inspire significant developments in mathematics and physics while at the same time offering the prospect to contribute to future quantum technology.

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“…The exploitation of energy resources significantly involve the study of the energy transfer, storage and generation. Recently, it attracts enormous attention to study quantum heat engine [5,6] and refrigeration [7][8][9][10], energy storage and transfer in quantum mechanical systems. The latter are named as "quantum battery" [11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Lower and upper bounds of quantum battery power in multiple central spin systems

Peng,

He,

Chesi

et al. 2021

Preprint

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We study the energy transfer process in quantum battery systems consisting of multiple central spins and bath spins. Here with "quantum battery" we refer to the central spins, whereas the bath serves as the "charger". For the single central-spin battery, we analytically derive the time evolutions of the energy transfer and the charging power with arbitrary number of bath spins. For the case of multiple central spins in the battery, we find the scaling-law relation between the maximum power Pmax and the number of central spins NB. It approximately satisfies a scaling law relation Pmax ∝ N α B , where scaling exponent α varies with the bath spin number N from the lower bound α = 1/2 to the upper bound α = 3/2. The lower and upper bounds correspond to the limits N → 1 and N ≫ NB, respectively. In thermodynamic limit, by applying the Holstein-Primakoff (H-P) transformation, we rigorously prove that the upper bound is Pmax = 0.72BA √ N N 3/2B , which shows the same advantage in scaling of a recent charging protocol based on the Tavis-Cummins model. Here B and A are the external magnetic field and coupling constant between the battery and the charger.

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Grüneisen parameters for the Lieb-Liniger and Yang-Gaudin models

Cited by 10 publications

References 50 publications

Grüneisen parameters: Origin, identity, and quantum refrigeration

Grüneisen parameters: Origin, identity, and quantum refrigeration

New trends in quantum integrability: Recent experiments with ultracold atoms

Lower and upper bounds of quantum battery power in multiple central spin systems

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