Bose–Einstein condensation in random potentials

Lenoble, O.; Pastur, L. А.; Zagrebnov, Valentin A.

doi:10.1016/j.crhy.2004.01.002

Cited by 28 publications

(35 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…for any l. Since the system is disordered, the unique solution µ ω l := µ ω l (β, ρ) of this equation is a random variable, which is a. s. non-random in the TL [4,6]. In the rest of this paper we denote the non-random µ ∞ := a. s.-lim l→∞ µ ω l .…”

Section: Generalized Bec In One-particle Random Eigenstatesmentioning

confidence: 99%

“…where ρ denotes a (fixed) mean density [4,6]. Physically, this corresponds to the macroscopic occupation of the set of eigenstates φ i with energy close to the ground state φ 1 .…”

Section: Generalized Bec In One-particle Random Eigenstatesmentioning

confidence: 99%

“…The authors conjectured a macroscopic occupation of the random ground state, but this was not rigorously proved until [5,6]. Although the free Bose-gas (i. e., the perfect gas without external potential or traps) does not exhibit BEC for dimension less than three, the randomness can enhance BEC even in one dimension, see [4]. This striking phenomenon is a consequence of the exponential decay of the one particle density of states at the bottom of the spectrum, known as Lifshitz tails, or "doublelogarithmic" asymptotics, which is generally believed to be associated with the existence of localized eigenstates [12].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bose condensation in (random) traps

Jaeck¹,

Pulé²,

Zagrebnov³

2009

Condens. Matter Phys.

View full text Add to dashboard Cite

We study a non-interacting (perfect) Bose-gas in random external potentials (traps). It is shown that a generalized Bose-Einstein condensation in the random eigenstates manifests if and only if the same occurs in the one-particle kinetic-energy eigenstates, which corresponds to the generalized condensation of the free Bose-gas. Moreover, we prove that the amounts of both condensate densities are equal. This statement is relevant for justification of the Bogoliubov approximation in the theory of disordered boson systems.

show abstract

Section: Generalized Bec In One-particle Random Eigenstatesmentioning

confidence: 99%

“…where ρ denotes a (fixed) mean density [4,6]. Physically, this corresponds to the macroscopic occupation of the set of eigenstates φ i with energy close to the ground state φ 1 .…”

Section: Generalized Bec In One-particle Random Eigenstatesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Bose condensation in (random) traps

Jaeck¹,

Pulé²,

Zagrebnov³

2009

Condens. Matter Phys.

View full text Add to dashboard Cite

show abstract

“…Since µ L (β, ρ) < ǫ * 1 (L), we can use the uniform convergence (9) to obtain the asymptotics of the solution of eq. (13) …”

mentioning

confidence: 99%

“…One can also switch in an external local attractive potential producing bound state(s) below the inf σ(t) = E 1 , the continuum spectrum [8]. A less obvious way is a suppression of the density states at the bottom of the spectrum, leading to convergence of the integral (4) for µ = E 1 , by embedding the PBG into a random external potential [9].…”

mentioning

confidence: 99%

Bose–Einstein condensation in geometrically deformed tubes

Exner

Zagrebnov

2005

J. Phys. A: Math. Gen.

View full text Add to dashboard Cite

show abstract

Fifteen Years of Microcavity Polaritons

Savona

2006

The Physics of Semiconductor Microcavities

View full text Add to dashboard Cite

In semiconductors with a direct interband optical transition, the fundamental electronic excitations above the ground state are excitons, namely hydrogen-like bound electron-hole pairs. In a perfect bulk semiconductor material, however, a correct description of the excited states must include the linear coupling of excitons to the electromagnetic field. This coupling gives rise to normal modes that are linear superpositions of one exciton and one photon mode, called exciton-polaritons . Exciton-polaritons are the actual excited states of a bulk semiconductor.Bulk polaritons were suggested in 1958 by J. Hopfield [58] and measured a few years later by means of non-linear optical spectroscopy [2,52,57,152]. The normal-mode coupling for polaritons is aresult of momentum conservation in the exciton-photon interaction. This selection rule imposes a one-to-one coupling between exciton and photon modes having the same momentum. As a consequence, within the linear coupling regime, the situation is analogous to that of two linearlycoupled harmonic oscillators. Two normal modes at different energies, the upper and the lower polariton, are formed. Due to the very different exciton and photon energy dispersion, as a function of momentum, polariton modes display an anticrossing with a minimum energy separation that can be as large as 16 meV in bulk GaAs [2]. Within the anticrossing region, polaritons are full admixtures of exciton and photon modes, while they have pure exciton or photon character far from it.The concept of polaritons remained linked to the physics of bulk semiconductors for more than two decades. The progress in fabrication of epitaxial semiconductor heterostructures, particularly quantum wells (QWs) led naturally to a description of their electronic excitations in terms of the polariton concept. However, because of the mismatch in the dimensionality of excitons (2D) and photons (3D), momentum conservation applies only to the in-plane component, and one exciton mode couples to a continuum of photon modes, resulting in an irreversible radiative decay instead of a normal-mode coupling [6,44]. Only at larger in-plane momenta, photon modes that are evanescent in the direction orthogonal to the QW can form surface polari- Physics of Semiconductor Microcavities: From Fundamentals toNanoscale DevicesEdited by Benoit Deveaud

show abstract

Bose–Einstein condensation in random potentials

Cited by 28 publications

References 24 publications

Bose condensation in (random) traps

Bose condensation in (random) traps

Bose–Einstein condensation in geometrically deformed tubes

Fifteen Years of Microcavity Polaritons

Contact Info

Product

Resources

About