QUANTUM COHOMOLOGY OF BLOWUPS OF SURFACES AND ITS FUNCTORIALITY PROPERTY

In this article, using the WDVV equation,the author first proves that all Gromov-Witten invariants of blowups of surfaces can be computed from the Gromov-Witten invariants of itself by some recursive relations. Furthermore, it may determine the quantum product on blowups. It also proves that there is some degree of functoriality of the big quantum cohomology for a blowup.     

VALUATIONS ON QUANTUM DIVISION RINGS

In the paper we determine all valuation on division rings of quantum polynomial rings (quantum fields). Furthermore we consider completions of quantum fields with respect to maximal valuations and study their automorphism groups and derivations.     

Quantum computation with scattering matrices

We discuss possible applications of the 1D direct and inverse scattering problem to the design of universal quantum gates for quantum computation. The potentials generating some universal gates are described. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 44, Quantum Computing, 2007.     

量子金融的意义

金融市场中的风险资产的演化过程遵从某种统计规律。这种统计规律通常是采用经典概率理论来加以阐述的。最近, 作者提出了从量子力学的角度来探讨金融问题的设想［1］,［2］,［3］。其中, 作者不仅从量子力学的角度用Maxwell Boltzmann统计重新推导了著名的Cox Ross Rubinstein期权定价公式，而且还用量子力学中的Bose Einstein统计(不可分辨粒子模型)得到了一个新的期权定价公式。这表明在理论上存在着一套关于金融市场的和谐的“量子理论”——量子金融。本文从对冲的角度来阐述这种潜在理论的金融意义和可能的实际内涵。作者给出了对冲定价的量子方案，详细讨论了单期金融市场的量子对冲问题。最后，作者解释了为什么（某些）金融市场在物理上要遵循量子规律，而不是经典统计规律。     

QUANTUM UNIQUE FACTORISATION DOMAINS

We prove a general theorem showing that iterated skew polynomialextensions of the type that fit the conditions needed by Cauchon'sdeleting derivations theory and by the Goodearl–Letzterstratification theory are unique factorisation rings in thesense of Chatters and Jordan. This general result applies tomany quantum algebras; in particular, generic quantum matricesand quantized enveloping algebras of the nilpotent part of asemisimple Lie algebra are unique factorisation domains in thesense of Chatters. The result also extends to generic quantumgrassmannians (by using noncommutative dehomogenisation) andto the quantum groups     

SOME PROBLEMS IN RADIATION TRANSPORT FLUID MECHANICS AND QUANTUM FLUID MECHANICS

We introduce the radiation transport equations, the radiation fluid mechanics equations and the fluid mechanics equations with quantum effects. We obtain the unique global weak solution for the radiation transport fluid mechanics equations under certain initial and boundary values. In addition, we also obtain the periodic region problem of the compressible N-S equation with quantum effect has weak solutions under some conditions.     

REPRESENTATIONS OF A LOOP LIE ALGEBRA ASSOCIATED WITH QUANTUM PLANE

In this article,some modules over a loop Lie algebra associated to quantum plane are constructed.The isomorphism classes among these modules are also determined.     

QUANTUM SUPERGROUPS I. FOUNDATIONS

In this part one of a series of papers, we introduce a new version of quantum covering and super groups with no isotropic odd simple root, which is suitable for the study of integrable modules, integral forms, and the bar involution. A quantum covering group involves parameters q and π with π²?=?1, and it specializes at π?=??1 to a quantum supergroup. Following Lusztig, we formulate and establish various structural results of the quantum covering groups, including a bilinear form, quasi- $ \mathcal{R} $ -matrix, Casimir element, character formulas for integrable modules, and higher Serre relations.     

A novel parallel quantum genetic algorithm for stochastic job shop scheduling

In this paper, a Novel Parallel Quantum Genetic Algorithm (NPQGA) is proposed for the stochastic Job Shop Scheduling Problem with the objective of minimizing the expected value of makespan, where the processing times are subjected to independent normal distributions. Based on the parallel evolutionary idea and some concepts of quantum theory, we simulate a model of parallel quantum computation. In this frame, there are some demes (sub-populations) and some universes (groups of populations), which are structured in super star-shaped topologies. A new migration scheme based on penetration theory is developed to control migration rate and direction adaptively between demes, and a novel quantum crossover strategy is devised among universes. The quantum evolution is executed in every deme by applying some improvement operators (the coding mechanism aiming at job shop, the new quantum rotation angle and the catastrophe operator). Experiment results show NPQGA's effectiveness and applicability.     

GLOBAL EXISTENCE OF WEAK SOLUTIONS TO THE THREE-DIMENSIONAL FULL COMPRESSIBLE QUANTUM EQUATIONS

We consider the quantum Navier-Stokes equations for the viscous, compressible, heat conducting fluids on the three-dimensional torus T~3. The model is based on a system which is derived by Jungel, Matthes and Milisic [15]. We made some adjustment about the relation of the viscosities of quantum terms.The viscosities and the heat conductivity coefficient are allowed to depend on the density, and may vanish on the vacuum. By several levels of approximation we prove the global-in-time existence of weak solutions for the large initial data.     

A Quantum Version of Spectral Decomposition Theorem of dynamical systems,quantum chaos hierarchy: Ergodic,mixing and exact

In this paper we study Spectral Decomposition Theorem (Lasota and Mackey, 1985) and translate it to quantum language by means of the Wigner transform. We obtain a Quantum Version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct goals: First, to rank Quantum Ergodic Hierarchy levels (Castagnino and Lombardi, 2009, Gomez and Castagnino, 2014). Second, to analyze the classical limit in quantum ergodic systems and quantum mixing systems. And third, and maybe most important feature, to find a relevant and simple connection between the first three levels of Quantum Ergodic Hierarchy (ergodic, exact and mixing) and quantum spectrum. Finally, we illustrate the physical relevance of QSDT applying it to two examples: Microwave billiards (Stockmann, 1999, Stoffregen et al. 1995) and a phenomenological Gamow model type (Laura and Castagnino, 1998, Omnès, 1994).     

THE WELL-POSEDNESS AND ASYMPTOTICS OF MULTI-DIMENSIONAL QUANTUM HYDRODYNAMICS

The multi-dimensional quantum hydrodynamic equations for charge transport in ultra-small electronic devices like semiconductors, where quantum effects （like particle tunnelling through potential barriers and built-up in quantum wells） take place, is considered in the present paper, and the recent progress on well-posedness, stability analysis, and small scaling limits are reviewed.     

一维半导体量子能量输运模型稳态解的唯一性

本文研究了一维半导体稳态量子能量输运模型的古典解.利用一些不等式技巧证明了当晶格温度充分大且电流密度较小时其解是唯一的,这在文献[3]中没有得到.     

Quantumness of quantum ensembles

Quantum ensembles, as generalizations of quantum states, are a universal instrument for describing the physical or informational status in measurement theory and communication theory because of the ubiquitous presence of incomplete information and the necessity of encoding classical messages in quantum states. The interrelations between the constituent states of a quantum ensemble can display more or less quantum characteristics when the involved quantum states do not commute because no single classical basis diagonalizes all these states. This contrasts sharply with the situation of a single quantum state, which is always diagonalizable. To quantify these quantum characteristics and, in particular, to more clearly understand the possibilities of secure data transmission in quantum cryptography, based on certain prototypical quantum ensembles, we introduce some figures of merit quantifying the quantumness of a quantum ensemble, review some existing quantities that are interpretable as measures of quantumness, and investigate their fundamental properties such as subadditivity and concavity. Comparing these measures, we find that different measures can yield different quantumness orderings for quantum ensembles. This reveals the elusive and complex nature of quantum ensembles and shows that no unique measure can describe all the fundamental and subtle properties of quantumness.     

OPTIMAL DECAY RATE OF THE COMPRESSIBLE QUANTUM NAVIER-STOKES EQUATIONS

For quantum fluids governed by the compressible quantum Navier-Stokes equations in $\Bbb R^3$ with viscosity and heat conduction, we prove the optimal $L^p-L^q$ decay rates for the classical solutions near constant states. The proof is based on the detailed linearized decay estimates by Fourier analysis of the operators, which is drastically different from the case when quantum effects are absent.     

环Fq+uFq+vFq上的循环码和量子码

本文研究了环R=F_q+uF_q+vF_q(u²=u,v²=v,uv=vu=0)上的循环码构造量子码的方法.利用环R上循环码的分解与生成多项式,给出了R上一个循环码可以构造量子码的一个充要条件.作为这类循环码的应用,得到了新的非二元量子码.     

Randomized and quantum algorithms yield a speed-up for initial-value problems

Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration and approximation problems, for which a speed-up is shown in many important cases by quantum computers with respect to deterministic and randomized algorithms on a classical computer. In this paper, we deal with the randomized and quantum complexity of initial-value problems. For this nonlinear problem, we show that both randomized and quantum algorithms yield a speed-up over deterministic algorithms. Upper bounds on the complexity in the randomized and quantum settings are shown by constructing algorithms with a suitable cost, where the construction is based on integral information. Lower bounds result from the respective bounds for the integration problem.     

Construction of some new quantum MDS codes

Quantum maximum-distance-separable (MDS) codes are an important class of quantum codes. In this paper, we mainly apply a new method of classical Hermitian self-orthogonal codes to construct three classes of new quantum MDS codes, and these quantum MDS codes provide large minimum distance.     

靶流形为球面子流形的调和映射的量子化现象(英文)

本文研究了调和映射和极小子流形的量子化性质.通过运用谱分解方法,获得了靶流形为球面子流形的调和映射的量子化性质,然后将其应用到球面的极小子流形的高斯映射,得到了极小子流形的第二基本形式的量子化性子.