Displaying similar documents to “From Planck to Ramanujan : a quantum 1 / f noise in equilibrium”

Identification of a localized source in an interstellar cloud: an inverse problem

Meri Lisi, Silvia Totaro (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We study an inverse problem for photon transport in an interstellar cloud. In particular, we evaluate the position x 0 of a localized source q ⁢ x = q 0 ⁢ δ ⁢ x - x 0 , inside a nebula (for example, a star). We assume that the photon transport phenomenon is one-dimensional. Since a nebula moves slowly in time, the number of photons U inside the cloud changes slowly in time. For this reason, we consider the so-called quasi-static approximation u to the exact solution U . By using semigroup theory, we prove existence...

The atomic and molecular nature of matter.

Charles L. Fefferman (1985)

Revista Matemática Iberoamericana

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The purpose of this article is to show that electrons and protons, interacting by Coulomb forces and governed by quantum statistical mechanics at suitable temperature and density, form a gas of Hydrogen atoms or molecules.

Isomorphic classification of the tensor products E ₀ ( e x p α i ) ⊗ ̂ E ∞ ( e x p β j )

Peter Chalov, Vyacheslav Zakharyuta (2011)

Studia Mathematica

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It is proved, using so-called multirectangular invariants, that the condition αβ = α̃β̃ is sufficient for the isomorphism of the spaces E ₀ ( e x p α i ) ⊗ ̂ E ∞ ( e x p β j ) and E ₀ ( e x p α ̃ i ) ⊗ ̂ E ∞ ( e x p β ̃ j ) . This solves a problem posed in [14, 15, 1]. Notice that the necessity has been proved earlier in [14].

A note on the Ehrhard inequality

Rafał Latała (1996)

Studia Mathematica

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We prove that for λ ∈ [0,1] and A, B two Borel sets in ℝ n with A convex, Φ - 1 ( γ n ( λ A + ( 1 - λ ) B ) ) ≥ λ Φ - 1 ( γ n ( A ) ) + ( 1 - λ ) Φ - 1 ( γ n ( B ) ) , where γ n is the canonical gaussian measure in ℝ n and Φ - 1 is the inverse of the gaussian distribution function.

Quasiconformal mappings and exponentially integrable functions

Fernando Farroni, Raffaella Giova (2011)

Studia Mathematica

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We prove that a K-quasiconformal mapping f:ℝ² → ℝ² which maps the unit disk onto itself preserves the space EXP() of exponentially integrable functions over , in the sense that u ∈ EXP() if and only if u ∘ f - 1 ∈ E X P ( ) . Moreover, if f is assumed to be conformal outside the unit disk and principal, we provide the estimate 1 / ( 1 + K l o g K ) ≤ ( | | u ∘ f - 1 | | E X P ( ) ) / ( | | u | | E X P ( ) ) ≤ 1 + K l o g K for every u ∈ EXP(). Similarly, we consider the distance from L ∞ in EXP and we prove that if f: Ω → Ω’ is a K-quasiconformal mapping and G ⊂ ⊂ Ω, then 1 / K ≤ ( d i s t E X P ( f ( G ) ) ( u ∘ f - 1 , L ∞ ( f ( G ) ) ) ) / ( d i s t E X P ( f ( G ) ) ( u , L ∞ ( G ) ) ) ≤ K for every u ∈ EXP(). We also...

Fast rotating Bose-Einstein condensates and Bargmann transform

Xavier Blanc (2005-2006)

Séminaire Équations aux dérivées partielles

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When a Bose-Einstein condensate (BEC) is rotated sufficiently fast, it nucleates vortices. The system is only stable if the rotational velocity Ω is lower than a critical value Ω c . Experiments show that as Ω approaches Ω c , the condensate nucleates more and more vortices, which become periodically arranged. We present here a mathematical study of this limit. Using Bargmann transform and an analogy with semi-classical analysis in second quantization, we prove that the system necessarily...