scholarly journals HYDRODYNAMICS OF THE VACUUM

2006 ◽  
Vol 21 (13n14) ◽  
pp. 2877-2903 ◽  
Author(s):  
P. M. STEVENSON
Keyword(s):  
Soliton Solutions ◽  
Empty Space ◽  
Effective Theory ◽  
Pitaevskii Equation ◽  
Hydrodynamic Equations ◽  
Wave Regime ◽  
Hydrodynamic Description ◽  
Normal Medium ◽  
Fluid Medium ◽  
Vacuum Case

Hydrodynamics is the appropriate "effective theory" for describing any fluid medium at sufficiently long length scales. This paper treats the vacuum as such a medium and derives the corresponding hydrodynamic equations. Unlike a normal medium the vacuum has no linear sound-wave regime; disturbances always "propagate" nonlinearly. For an "empty vacuum" the hydrodynamic equations are familiar ones (shallow water-wave equations) and they describe an experimentally observed phenomenon — the spreading of a clump of zero-temperature atoms into empty space. The "Higgs vacuum" case is much stranger; pressure and energy density, and hence time and space, exchange roles. The speed of sound is formally infinite, rather than zero as in the empty vacuum. Higher-derivative corrections to the vacuum hydrodynamic equations are also considered. In the empty-vacuum case the corrections are of quantum origin and the post-hydrodynamic description corresponds to the Gross–Pitaevskii equation. We conjecture the form of the post-hydrodynamic corrections in the Higgs case. In the (1+1)-dimensional case the equations possess remarkable "soliton" solutions and appear to constitute a new exactly integrable system.

scholarly journals EFFECTIVE FIELD THEORY OF IDEAL-FLUID HYDRODYNAMICS

1996 ◽  
Vol 10 (21) ◽  
pp. 999-1010 ◽  
Author(s):  
ADRIAAN M.J. SCHAKEL
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Effective Field ◽  
Effective Theory ◽  
Goldstone Mode ◽  
Hydrodynamic Equations ◽  
Standard Description ◽  
Spontaneous Breakdown ◽  
Sound Mode ◽  
Fluid Hydrodynamics

Starting from a standard description of an ideal, isentropic fluid, we derive the effective theory governing a gapless non-relativistic mode — the sound mode. The theory, which is dictated by the requirement of Galilei invariance, entails the entire set of hydrodynamic equations. The gaplessness of the sound mode is explained by identifying it as the Goldstone mode associated with the spontaneous breakdown of Galilei invariance. Differences with a superfluid are pointed out.

scholarly journals FLAVOR-CONSERVING OSCILLATIONS OF DIRAC-MAJORANA NEUTRINOS

1998 ◽  
Vol 13 (29) ◽  
pp. 5023-5036 ◽  
Author(s):  
SALVATORE ESPOSITO
Keyword(s):  
Transition Probability ◽  
Normal Medium ◽  
Resonant Enhancement ◽  
Vacuum Case ◽  
Helicity Conservation ◽  
Majorana Neutrinos

We analyze both chirality-changing and chirality-preserving transitions of Dirac–Majorana neutrinos. In vacuum, the first ones are suppressed with respect to the others due to helicity conservation and the interactions with a ("normal") medium practically does not affect the expressions of the probabilities for these transitions, even if the amplitudes of oscillations change slightly. For usual situations involving relativistic neutrinos we find no resonant enhancement for all flavor-conserving transitions. However, for very light neutrinos propagating in superdense media, the pattern of oscillations [Formula: see text] is dramatically altered with respect to the vacuum case, the transition probability practically vanishing. An application of this result is envisaged.

Dynamics of matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions and gain or loss effect

2022 ◽  
Author(s):  
Yajie Yang ◽  
Ying Dong
Keyword(s):  
Similarity Transformation ◽  
Soliton Solutions ◽  
Gain Coefficient ◽  
Loss Coefficient ◽  
Matter Wave ◽  
Pitaevskii Equation ◽  
Loss Parameter ◽  
Dynamical Properties ◽  
Bose Einstein ◽  
Loss Effect

Abstract The gain or loss effect on the dynamics of the matter-wave solitons in three-component Bose-Einstein condensates with time-modulated interactions trapped in parabolic external potentials are investigated analytically. Some exact matter-wave soliton solutions to the three-coupled Gross-Pitaevskii equation describing the three-component Bose-Einstein condensates are constructed by similarity transformation. The dynamical properties of the matter-wave solitons are analyzed graphically, and the effects of the gain or loss parameter and the frequency of the external potentials on the matter-wave solitons are explored. It is shown that the gain coefficient makes the atom condensate to absorb energy from the background, while the loss coefficient brings about the collapse of the condensate.

scholarly journals Superfluid light in bulk nonlinear media

2014 ◽  
Vol 470 (2169) ◽  
pp. 20140320 ◽  
Author(s):  
Iacopo Carusotto
Keyword(s):  
Order Parameter ◽  
Light Propagation ◽  
Pitaevskii Equation ◽  
Sound Waves ◽  
Many Body ◽  
Hydrodynamic Description ◽  
Nonlinear Media ◽  
Analogue Models ◽  
The Many ◽  
Models Of Gravity

We review how the paraxial approximation naturally leads to a hydrodynamic description of light propagation in a bulk Kerr nonlinear medium in terms of a wave equation analogous to the Gross–Pitaevskii equation for the order parameter of a superfluid. The main features of the many-body collective dynamics of the fluid of light in this propagating geometry are discussed: generation and observation of Bogoliubov sound waves in the fluid of light is first described. Experimentally accessible manifestations of superfluidity are then highlighted. Perspectives in view of realizing analogue models of gravity are finally given.

scholarly journals Soliton Solutions and Collisions for the Multicomponent Gross–Pitaevskii Equation in Spinor Bose–Einstein Condensates

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Ming Wang ◽  
Guo-Liang He
Keyword(s):  
Soliton Solutions ◽  
Auxiliary Function ◽  
Einstein Condensate ◽  
Polarization Parameter ◽  
One Dimension ◽  
Pitaevskii Equation ◽  
Bose Einstein Condensate ◽  
The One ◽  
Bose Einstein ◽  
Two Peaks

In this paper, we investigate a five-component Gross–Pitaevskii equation, which is demonstrated to describe the dynamics of an F=2 spinor Bose–Einstein condensate in one dimension. By employing the Hirota method with an auxiliary function, we obtain the explicit bright one- and two-soliton solutions for the equation via symbolic computation. With the choice of polarization parameter and spin density, the one-soliton solutions are divided into four types: one-peak solitons in the ferromagnetic and cyclic states and one- and two-peak solitons in the polar states. For the former two, solitons share the similar shape of one peak in all components. Solitons in the polar states have the one- or two-peak profiles, and the separated distance between two peaks is inversely proportional to the value of polarization parameter. Based on the asymptotic analysis, we analyze the collisions between two solitons in the same and different states.

scholarly journals On the linear wave regime of the Gross-Pitaevskii equation

2010 ◽  
Vol 110 (1) ◽  
pp. 297-338 ◽  
Author(s):  
Fabrice Béthuel ◽  
Raphaël Danchin ◽  
Didier Smets
Keyword(s):  
Pitaevskii Equation ◽  
Linear Wave ◽  
Wave Regime

scholarly journals HOPF SOLITON SOLUTIONS FROM LOW ENERGY EFFECTIVE ACTION OF SU(2) YANG–MILLS THEORY

2006 ◽  
Vol 21 (15) ◽  
pp. 1189-1202 ◽  
Author(s):  
NOBUYUKI SAWADO ◽  
NORIKO SHIIKI ◽  
SHINGO TANAKA
Keyword(s):  
Fourth Order ◽  
Effective Action ◽  
Dimensional Space ◽  
Soliton Solutions ◽  
Low Energy ◽  
Effective Theory ◽  
Second Derivative ◽  
Yang Mills ◽  
Extended Action ◽  
Derivative Term

The Skyrme–Faddeev–Niemi (SFN) model which is an O(3) σ-model in three-dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang–Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang–Mills theory recovers the SFN in the infrared region. However, the theory contains another fourth-order term which destabilizes soliton solutions. We find the stable soliton solutions in this extended action, introducing a second derivative term as a stabilizer. A perturbative technique for the second derivative term is applied to exclude (or reduce) the ill behavior of the action. A new topological energy bound formula is inferred for the action.

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