Statistical Mechanics of One-Dimensional Ginzburg-Landau Fields

Scalapino, D. J.; Sears, Matthew R.; Ferrell, Richard A.

doi:10.1103/physrevb.6.3409

Cited by 510 publications

(237 citation statements)

References 12 publications

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“…As was the case for the φ 8 field theories considered above, there are once again potentials for which the RHS of the dispersion relation vanishes; but, it cannot vanish in the other cases due to our assumption b > a. Using the transfer matrix technique, it was shown by Scalapino et al [33,34] that, in the thermodynamic limit, the classical free energy of a given field theory is essentially given by the ground state energy of the Schrödinger-like equation whose potential is given by the field theory's potential V (φ). Now, it is well known that while the ground state energy cannot be obtained analytically if the leading term of the potential is of the form φ 4n with n = 1, 2, .…”

Section: F Phononsmentioning

confidence: 98%

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

2014

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We obtain exact solutions for kinks in φ 8 , φ 10 and φ 12 field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed exponentialalgebraic tail decay, unlike the lower-order φ 4 and φ 6 theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the co-existence of up to three distinct kinks (for a φ 12 potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the φ 10 field theory, which is a quasi-exactly solvable (QES) model akin to φ 6 , we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.

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Section: F Phononsmentioning

confidence: 98%

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

2014

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“…In the weakly interacting regime at low T , where the density fluctuations are suppressed and the phase fluctuates on a distance scale much larger than the correlation length l c , one can speak of a phase-fluctuating Bose-condensed state (quasicondensate). A 1D classical field model for calculating correlation functions in the conditions, where both the density and phase fluctuations are important, was developed in [50] and for Bose gases in [51]. The use of the Bogoliubov approach for describing 1D uniform (quasi)condensates is recently discussed in [52] and is presented in the lectures of Yvan Castin.…”

Section: Lecture 3 True and Quasicondensates In 1d Trapped Gasesmentioning

confidence: 99%

Low-dimensional trapped gases

2004

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Recent developments in the physics of ultracold gases provide wide possibilities for reducing the dimensionality of space for magnetically or optically trapped atoms. The goal of these lectures is to show that regimes of quantum degeneracy in two-dimensional (2D) and one-dimensional (1D) trapped gases are drastically different from those in three dimensions and to stimulate an interest in low-dimensional systems. Attention is focused on the new physics appearing in currently studied low-dimensional trapped gases and related to finite-size and finite-temperature effects.

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“…The partition function for the classical 0D XY model (Eq. 5), can be written in a transfer-matrix form (see for example [17]) as Z XY = T r[M N (φ − φ ′ )] where M (φ) = eJ cos φ = n I n (J )e inφ , and I n (x) are modified Bessel functions. The equilibrium momentum distribution of the bosons for the N = ∞ lattice is calculated to be…”

Section: D Mott Insulatorsmentioning

confidence: 99%

Quench-induced Mott-insulator-to-superfluid quantum phase transition

Wang

Sarma

2012

Phys. Rev. A

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Mott insulator to superfluid quenches have been used by recent experiments to generate exotic superfluid phases. While the final Hamiltonian following the sudden quench is that of a superfluid, it is not apriori clear how close the final state of the system approaches the ground state of the superfluid Hamiltonian. To understand the nature of the final state we calculate the temporal evolution of the momentum distribution following a Mott insulator to superfluid quench. Using the numerical infinite time-evolving block decimation approach and the analytical rotor model approximation we establish that the one and two dimensional Mott insulators following the quench equilibriate to thermal states with spatially short-ranged coherence peaks in the final momentum distribution and therefore are not strict superfluids. However, in three dimensions we find a divergence in the momentum distribution indicating the emergence of true superfluid order.

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Statistical Mechanics of One-Dimensional Ginzburg-Landau Fields

Cited by 510 publications

References 12 publications

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

Low-dimensional trapped gases

Quench-induced Mott-insulator-to-superfluid quantum phase transition

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