Directed polymers in high dimensions

We study directed polymers subject to a quenched random potential in d transversal dimensions. This system is closely related to the Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation theory we show that physical quantities develop singular behavior for d to 4. For example, the universal finite size amplitude of the free energy at the roughening transition is proportional to (4-d)^(1/2). This shows that the dimension d=4 plays a special role for this system and points towards d=4 as the upper critical dimension of the Kardar-Parisi-Zhang problem.Comment: 37 pages REVTEX including 4 PostScript figure

Universality classes of the Kardar-Parisi-Zhang equation

We re-examine mode-coupling theory for the Kardar-Parisi-Zhang (KPZ) equation in the strong coupling limit and show that there exists two branches of solutions. One branch (or universality class) only exists for dimensionalities $d<d_c=2$ and is similar to that found by a variety of analytic approaches, including replica symmetry breaking and Flory-Imry-Ma arguments. The second branch exists up to $d_c=4$ and gives values for the dynamical exponent $z$ similar to those of numerical studies for $d\ge2$.Comment: 4 pages, 1 figure, published versio

Manni Zhang, soprano and Anna Carl, piano, April 21, 2018

This is the concert program of the Manni Zhang, soprano and Anna Carl, piano performance on Saturday, April 21, 2018 at 8:00 p.m., at the Concert Hall, 855 Commonwealth Avenue. Works performed were La Promessa by Gioachino Rossini, Fiocca La Neve nu Pietro Cimara, Stornello by P. Cimara, Perchè dolce, caro bene by Stefano Donaudy, Ganymed Op. 19, No. 3 D. 544 by Franz Schubert, Liebhaber in allen Gestalten D. 558 by F. Schubert, Im Abendroth D. 799 by F. Schubert, Die Forelle Op. 32 D. 550 by F. Schubert, Vorrei spiegarvi, O Dio by Wolfgang Amadeus Mozart, Fêtes galantes by Claude Debussy, En Sourdine by C. Debussy, Fantoches by C. Debussy, Clair De Lune by C. Debussy, Love by Vittorio Giannini, Tell me, Oh blue blue Sky! by V. Giannini, Sing to My Heart a Song by V. Giannini, and Spring Nostalgia by Huang Zi. Digitization for Boston University Concert Programs was supported by the Boston University Humanities Library Endowed Fund

Comment on "Conjectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices" [arXiv:0705.1045]

It is shown that a recent article by Z.-D. Zhang [arXiv:0705.1045] is in error and violates well-known theorems.Comment: LaTeX, 3 pages, no figures, submitted to Philosophical Magazine. Expanded versio

Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation

We present a simple approximation of the non-perturbative renormalization group designed for the Kardar-Parisi-Zhang equation and show that it yields the correct phase diagram, including the strong-coupling phase with reasonable scaling exponent values in physical dimensions. We find indications of a possible qualitative change of behavior around $d=4$. We discuss how our approach can be systematically improved.Comment: 4 pages, 1 figure, references added, minor change

Explicit eigenvalues of certain scaled trigonometric matrices

In a very recent paper "\emph{On eigenvalues and equivalent transformation of trigonometric matrices}" (D. Zhang, Z. Lin, and Y. Liu, LAA 436, 71--78 (2012)), the authors motivated and discussed a trigonometric matrix that arises in the design of finite impulse response (FIR) digital filters. The eigenvalues of this matrix shed light on the FIR filter design, so obtaining them in closed form was investigated. Zhang \emph{et al.}\ proved that their matrix had rank-4 and they conjectured closed form expressions for its eigenvalues, leaving a rigorous proof as an open problem. This paper studies trigonometric matrices significantly more general than theirs, deduces their rank, and derives closed-forms for their eigenvalues. As a corollary, it yields a short proof of the conjectures in the aforementioned paper.Comment: 7 pages; fixed Lemma 2, tightened inequalitie

Reply to Comment on ''Quantum key distribution for d-level systems with generalized Bell states''

In a recent comment \cite{ch1} it has been claimed that an entangled-based quantum key distribution protocol proposed in \cite{zhang} and its generalization to d-level systems in \cite{v1} are insecure against an attack devised by the authors of the comment. We invalidate the arguments of the comment and show that the protocols are still secure.Comment: 4 pages, Latex, no figures, Accepted for Publication in Phys. Rev.