On a Boltzmann equation for Haldane statistics

The study of quantum quasi-particles at low temperatures including their statistics, is a frontier area in modern physics. In a seminal paper F.D. Haldane proposed a definition based on a generalization of the Pauli exclusion principle for fractional quantum statistics. The present paper is a study of quantum quasi-particles obeying Haldane statistics in a fully non-linear kinetic Boltzmann equation model with large initial data on a torus. Strong L1 solutions are obtained for the Cauchy problem. The main results concern existence, uniqueness and stability. Depending on the space dimension and the collision kernel, the results obtained are local or global in time.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1406.0265 This is the published version of the paper. The condition (2.3) on the collision kernel is strengthened, as required for the result to hol

Well-posedness of the Cauchy problem for a space-dependent anyon Boltzmann equation

A fully non-linear kinetic Boltzmann equation for anyons and large initial data is studied in a periodic 1d setting. Strong L1 solutions are obtained for the Cauchy problem. The main results concern global existence, uniqueness, and stability.Comment: 22 pages. In this version an earlier error has been corrected, and with it a study of the time asymptotics moved to a future paper. arXiv admin note: text overlap with arXiv:1207.059

Fermat's principle in quantum gravitational optics

Interactions incorporating the vacuum polarization effects in curved backgrounds modify the null cone structure in such a way that the photon trajectories would not be the space-time geodesics anymore. The gravitational birefringence introduced as a direct consequence of these effects, will allow shifts in the photon velocities leading to polarization dependent superluminal propagation. Taking these effects into account we study Fermat's principle in the context of the 1+3 (threading) formulation of the space-time decomposition. We find an expression for the modified spacetime refractive index and show it is proportional to the light cone correction to the first order. Consequences of this modification on polarization sum rules and spatial light paths are considered.Comment: 13 Pages, REVTex format, section on gravitomagnetic monopoles is removed along with its references, new references adde

On the Cauchy problem with large data for the space-dependent Boltzmann Nordheim equation III

This paper studies the quantum Boltzmann Nordheim equation from a Boltzmann equation for Haldane statistics. Strong solutions are obtained for the Cauchy problem with initial data in L1 and uniformly bounded on a one (resp. two or three)-dimensional torus for three-dimensional velocities and pseudo-Maxwellian (resp. very soft) forces. The main results are existence, uniqueness and stability of solutions conserving mass, momentum, and energy, with the uniform bound exploding if the solutions are only local in time.Comment: 20 pages. arXiv admin note: text overlap with arXiv:1711.10357, arXiv:1601.06927, arXiv:1611.0747

On stationary solutions to normal, coplanar, discrete Boltzmann equation models

The paper proves existence of renormalized solutions for a class of velocity-discrete coplanar stationary Boltzmann equations with given indata. The proof is based on the construction of a sequence of approximations with L1 compactness for an integrated collision frequency and gain term. The compactness is obtained using the Kolmogorov Riesz theorem.Comment: to appear in Communications in Mathematical Science

Comparison of anti-Mullerian Hormone average between laparoscopic and treatment with clomiphene citrate in patients with polycystic ovarian syndrome

زمینه و هدف: آنتی مولرین هورمون (AMH) در پاتوژنز سندرم پلی کیستیک تخمدان درگیر می باشد. هدف ما مقایسه میانگین AMH در 2 روش لاپاروسکوپی و درمان با کلومیفن سیترات جهت سنجش پاسخ تخمدانی بود. روش بررسی: این مطالعه کارآزمایی بالینی بر روی زنان با سندرم پلی کیستیک تخمدان بدون تخمک گذاری انجام شد. بیماران به 2 گروه تحت مداوا با روش لاپاروسکوپی (49 نفر) و تحت درمان با کلومیفن سیترات (20 نفر) تقسیم گردیدند. غلظت های پلاسمایی AMH قبل از عمل و یک هفته بعد از آن و همچنین 3 و 6 ماه بعد از درمان انداره گیری شد. برای مقایسه میانگین ها در بین گروه ها از آنالیز ANOVA استفاده شد. یافته ها: میزان AMH قبل از مداوا در زنان تحت درمان با لاپاراسکوپی (1/4±1/6) و کلومیفن سیترات (2/3±7/5) تفاوت معنی دار نداشت (05/0<P). بعد از لاپاروسکوپی میزان AMH در بیماران پاسخ دهنده به درمان (1/2±6/5) در مقایسه با بیمارانی که به درمان پاسخ ندادند (3/1±9)، تفاوت معنی داری نشان داد (05/0>P). میزان AMH در بیماران تحت درمان کلومیفن سیترات در این مدت کاهش معنی داری نداشت. نتیجه گیری: درمان لاپاروسکوپی در بیمارانی که سطح AMH آن ها قبل از درمان پایین تر است، موفقیت آمیز می باشد