Integrable Families of Hard-Core Particles with Unequal Masses in a One-Dimensional Harmonic Trap

Harshman, N. L.; Olshanii, Maxim; Dehkharghani, Amin; Volosniev, A. G.; Jackson, Steven Glenn; Zinner, N. T.

doi:10.1103/physrevx.7.041001

Cited by 34 publications

(32 citation statements)

References 89 publications

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“…Quantum chaos [18] and thermalization with the appearance of the Fermi-Dirac distribution [21][22][23][24][25] were also obtained with just four interacting particles. More recently, thermalization was studied in systems with 5 particles [26] and quantum chaos was verified again in systems with only 4 particles [27][28][29][30], and possibly even with as few as 3 interacting particles [31]. However, it is not entirely clear if other indicators of chaos show similar behaviors, and if the obtained threshold of 4 interacting particles can be changed by the introduction of long-range interactions.…”

Section: Introductionmentioning

confidence: 99%

How many particles make up a chaotic many-body quantum system?

2021

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We numerically investigate the minimum number of interacting particles, which is required for the onset of strong chaos in quantum systems on a one-dimensional lattice with short-range and long-range interactions. We consider multiple system sizes which are at least three times larger than the number of particles and find that robust signatures of quantum chaos emerge for as few as 4 particles in the case of short-range interactions and as few as 3 particles for long-range interactions, and without any apparent dependence on the size of the system.

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Section: Introductionmentioning

confidence: 99%

How many particles make up a chaotic many-body quantum system?

2021

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“…The integrals of motion, including the third superintegral, should carry over without modification into quantum observables. In fact, mixed-mass superintegrability with hard-core interactions has been previously identified for quantum billiards in free space [26] and harmonic traps [42].…”

Section: Discussionmentioning

confidence: 86%

“…In the limit of large mass, Equations (42) and (43) coincide. We compare predictions of Equation (43) with the exact results in Figure 9.…”

Section: Position As a Function Of Time: Hyperbolic Shapementioning

confidence: 92%

The Dynamics of Digits: Calculating Pi with Galperin’s Billiards

et al. 2020

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In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number π . This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of π in a base determined by the ratio of the masses of the two particles. This base can be any integer, but it can also be an irrational number, or even the base can be π itself. This article reviews previous results for Galperin billiards and then pushes these results farther. We provide a complete explicit solution for the balls’ positions and velocities as a function of the collision number and time. We demonstrate that Galperin billiard can be mapped onto a two-particle Calogero-type model. We identify a second dynamical invariant for any mass ratio that provides integrability for the system, and for a sequence of specific mass ratios we identify a third dynamical invariant that establishes superintegrability. Integrability allows us to derive some new exact results for trajectories, and we apply these solutions to analyze the systematic errors that occur in calculating the digits of π with Galperin billiards, including curious cases with irrational number bases.

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“…To that end, we consider the SU(4) fermionic gas with N = 4 and internal states labeled as |↑〉, |↗〉, |↘〉 and |↓〉. The number of particles in each state is thus given by (the so-called 1 + 1 + 1 + 1 infinitely repulsive system with different masses is known to have interesting properties, which were described in 66 ). We rewrite the permutation operator for the SU(4) system as…”

Section: Resultsmentioning

confidence: 99%

Dynamics of spin and density fluctuations in strongly interacting few-body systems

Barfknecht¹,

Foerster²,

Zinner³

2019

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The decoupling of spin and density dynamics is a remarkable feature of quantum one-dimensional many-body systems. In a few-body regime, however, little is known about this phenomenon. To address this problem, we study the time evolution of a small system of strongly interacting fermions after a sudden change in the trapping geometry. We show that, even at the few-body level, the excitation spectrum of this system presents separate signatures of spin and density dynamics. Moreover, we describe the effect of considering additional internal states with SU(N) symmetry, which ultimately leads to the vanishing of spin excitations in a completely balanced system.

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Integrable Families of Hard-Core Particles with Unequal Masses in a One-Dimensional Harmonic Trap

Cited by 34 publications

References 89 publications

How many particles make up a chaotic many-body quantum system?

How many particles make up a chaotic many-body quantum system?

The Dynamics of Digits: Calculating Pi with Galperin’s Billiards

Dynamics of spin and density fluctuations in strongly interacting few-body systems

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