Separation of the Interaction Potential into Two Parts in Treating Many‐Body Systems. I. General Theory and Applications to Simple Fluids with Short‐Range and Long‐Range Forces

1965 ◽  
Vol 6 (8) ◽  
pp. 1282-1298 ◽  
Author(s):  
J. L. Lebowitz ◽  
G. Stell ◽  
S. Baer
Keyword(s):  
General Theory ◽  
Long Range ◽  
Interaction Potential ◽  
Short Range ◽  
Many Body ◽  
Simple Fluids ◽  
Many Body Systems

scholarly journals Quantum-optical magnets with competing short- and long-range interactions: Rydberg-dressed spin lattice in an optical cavity

2016 ◽  
Vol 1 (1) ◽  
Author(s):  
Jan Gelhausen ◽  
Michael Buchhold ◽  
Achim Rosch ◽  
Philipp Strack
Keyword(s):  
Quantum Optics ◽  
Long Range ◽  
Short Range ◽  
Cold Atoms ◽  
Theoretical Modelling ◽  
Many Body ◽  
Spin Lattice ◽  
Long Range Interactions ◽  
Many Body Systems ◽  
Quantum Optical

The fields of quantum simulation with cold atoms and quantum optics are currently being merged. In a set of recent pathbreaking experiments with atoms in optical cavities , lattice quantum many-body systems with both, a short-range interaction and a strong interaction potential of infinite range –mediated by a quantized optical light field– were realized. A theoretical modelling of these systems faces considerable complexity at the interface of: (i) spontaneous symmetry-breaking and emergent phases of interacting many-body systems with a large number of atoms N\rightarrow \inftyN→∞, (ii) quantum optics and the dynamics of fluctuating light fields, and (iii) non-equilibrium physics of driven, open quantum systems. Here we propose what is possibly the simplest, quantum-optical magnet with competing short- and long-range interactions, in which all three elements can be analyzed comprehensively: a Rydberg-dressed spin lattice coherently coupled to a single photon mode. Solving a set of coupled even-odd sublattice master equations for atomic spin and photon mean-field amplitudes, we find three key results. (R1): Superradiance and a coherent photon field appears in combination with spontaneously broken magnetic translation symmetry. The latter is induced by the short-range nearest-neighbor interaction from weakly admixed Rydberg levels. (R2): This broken even-odd sublattice symmetry leaves its imprint in the light via a novel peak in the cavity spectrum beyond the conventional polariton modes. (R3): The combined effect of atomic spontaneous emission, drive, and interactions can lead to phases with anomalous photon number oscillations. Extensions of our work include nano-photonic crystals coupled to interacting atoms and multi-mode photon dynamics in Rydberg systems.

scholarly journals Order Indices and Entanglement Production in Quantum Systems

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 565 ◽  
Author(s):  
Vyacheslav I. Yukalov
Keyword(s):  
Long Range ◽  
Short Range ◽  
Quantum Systems ◽  
Quantum Operation ◽  
Many Body ◽  
Finite Systems ◽  
Production Order ◽  
Intimate Relation ◽  
Many Body Systems ◽  
Statistical Systems

The review is devoted to two important quantities characterizing many-body systems, order indices and the measure of entanglement production. Order indices describe the type of order distinguishing statistical systems. Contrary to the order parameters characterizing systems in the thermodynamic limit and describing long-range order, the order indices are applicable to finite systems and classify all types of orders, including long-range, mid-range, and short-range orders. The measure of entanglement production quantifies the amount of entanglement produced in a many-partite system by a quantum operation. Despite that the notions of order indices and entanglement production seem to be quite different, there is an intimate relation between them, which is emphasized in the review.

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

2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Guy Zisling ◽  
Lea Santos ◽  
Yevgeny Bar Lev
Keyword(s):  
Long Range ◽  
Quantum Chaos ◽  
Short Range ◽  
Many Body ◽  
Interacting Particles ◽  
One Dimensional ◽  
Long Range Interactions ◽  
Minimum Number ◽  
Many Particles ◽  
Number Of Particles

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.

EXISTENCE OF FOUR DISTINCT PHASES IN ONE DIMENSIONAL MANY-BODY SYSTEMS WITH LONG-RANGE INTERACTION: QUANTUM KOSTERLITZ–THOULESS TRANSITIONS

2001 ◽  
Vol 15 (06n07) ◽  
pp. 175-182
Author(s):  
KAZUMOTO IGUCHI
Keyword(s):  
Long Range ◽  
Luttinger Liquid ◽  
Scaling Theory ◽  
Wigner Crystal ◽  
Many Body ◽  
Range Interaction ◽  
One Dimensional ◽  
Ground State Wavefunction ◽  
Long Range Interaction ◽  
Many Body Systems

We conceptually study the existence of four distinct quantum phases: the Luttinger liquid, the Wigner crystal, the Coulomb plasma and the molecular crystal in one-dimensional many-body systems with long-range interaction. We show that the anomaly of the ground state wavefunction indicates a quantum Kosterlitz–Thouless transition at zero temperature, which separates into two regimes of the Luttinger liquid and the Wigner crystal. We also postulate a scaling theory which discriminate the four phases using the Kosterlitz–Thouless scaling theory.

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