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Qi Zhang

Publications and source records attributed to Qi Zhang.

1,164 records · Page 65Linked to original sources
arXiv2009

Proximity-induced superconductivity in nanowires: Mini-gap state and differential magnetoresistance oscillations

We study proximity-induced superconductivity in gold nanowires as a function of the length of the nanowire, magnetic field, and excitation current. Short nanowires exhibit a sharp superconducting transition, whereas long nanowires show nonzero resistance. At intermediate lengths, however, we observe two sharp transitions; the normal and superconducting regions are separated by what we call the mini-gap phase. Additionally, we detect periodic oscillations in the differential magnetoresistance. We provide a theoretical model for the mini-gap phase as well as the periodic oscillations in terms of the coexistence of proximity-induced superconductivity with a normal region near the center of the wire, created either by temperature or application of a magnetic field.

cond-mat.supr-con↗
arXiv2008

Stationary Solutions of SPDEs and Infinite Horizon BDSDEs

In this paper we study the existence of stationary solutions for stochastic partial differential equations. We establish a new connection between $L_ρ^2({\mathbb{R}^{d}};{\mathbb{R}^{1}}) \otimes L_ρ^2({\mathbb{R}^{d}};{\mathbb{R}^{d}})$ valued solutions of backward doubly stochastic differential equations (BDSDEs) on infinite horizon and the stationary solutions of the SPDEs. Moreover, we prove the existence and uniqueness of the solutions of BDSDEs on both finite and infinite horizons, so obtain the solutions of initial value problems and the stationary solutions (independent of any initial value) of SPDEs. The connection of the weak solutions of SPDEs and BDSDEs has independent interests in the areas of both SPDEs and BSDEs.

math.PR↗
arXiv2008

Stationary Solutions of SPDEs and Infinite Horizon BDSDEs with Non-Lipschitz Coefficients

We prove a general theorem that the $L_ρ^2({\mathbb{R}^{d}};{\mathbb{R}^{1}})\otimes L_ρ^2({\mathbb{R}^{d}};{\mathbb{R}^{d}})$ valued solution of an infinite horizon backward doubly stochastic differential equation, if exists, gives the stationary solution of the corresponding stochastic partial differential equation. We prove the existence and uniqueness of the $L_ρ^2({\mathbb{R}^{d}};{\mathbb{R}^{1}})\otimes L_ρ^2({\mathbb{R}^{d}};{\mathbb{R}^{d}})$ valued solutions for backward doubly stochastic differential equations on finite and infinite horizon with linear growth without assuming Lipschitz conditions, but under the monotonicity condition. Therefore the solution of finite horizon problem gives the solution of the initial value problem of the corresponding stochastic partial differential equations, and the solution of the infinite horizon problem gives the stationary solution of the SPDEs according to our general result.

math.PR↗
arXiv2008

Nonlinear Landau-Zener Processes in a Periodic Driving Field

Effects of a periodic driving field on Landau-Zener processes are studied using a nonlinear two-mode model that describes the mean-field dynamics of a many-body system. A variety of different dynamical phenomena in different parameter regimes of the driving field are discussed and analyzed. These include shifted, weakened, or enhanced phase dependence of nonlinear Landau-Zener processes, nonlinearity-enhanced population transfer in the adiabatic limit, and Hamiltonian chaos on the mean field level. The emphasis of this work is placed on how the impact of a periodic driving field on Landau-Zener processes with self-interaction differs from those without self-interaction. Aside from gaining understandings of driven nonlinear Landau-Zener processes, our findings can be used to gauge the strength of nonlinearity and for efficient manipulation of the mean-field dynamics of many-body systems.

cond-mat.other↗
arXiv2008

Singular symplectic flops and Ruan cohomology

In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient $$ W_r=\{(x,y,z,t)|xy-z^{2r}+t^2=0 \}/μ_r(a,-a,1,0), r\geq 1, $$ which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let $X$ and $Y$ be two symplectic orbifolds connected by such a flop. We study orbifold Gromov-Witten invariants of exceptional classes on $X$ and $Y$ and show that they have isomorphic Ruan cohomologies. Hence, we verify a conjecture of Ruan.

math.SG↗
arXiv2008

Two-mode Bose-Einstein condensate in a high-frequency driving field that directly couples the two modes

A two-mode Bose-Einstein condensate coupled by a high-frequency modulation field is found to display rich features. An effective stationary Hamiltonian approach reveals the emergence of additional degenerate eigenstates as well as new topological structures of the spectrum. Possible applications, such as the suppression of nonlinear Landau-Zener tunneling, are discussed. An interesting phenomenon, which we call "deterministic symmetry-breaking trapping" associated with separatrix crossing, is also found in an adiabatic process.

quant-ph↗
arXiv2008

Anomalous Monopole In an Interacting Boson System

Anomalous monopole of disk shape is found to exist in the semiclassical theory of a two-mode interacting boson system. The quantum origin of this anomaly is the collapsing or bundling of field lines of Berry curvature caused by the interaction between bosons in the semiclassical limit. The significance of this anomalous monopole is twofold: (1) it signals the failure of the von Neumann-Wigner theorem in the semiclassical limit; (2) it indicates a breakdown of the correspondence principle between quantum and classical dynamics.

cond-mat.other↗
arXiv2006

Vector Potential and Berry phase-induced Force

We present a general theoretical framework for the exact treatment of a hybrid system that is composed of a quantum subsystem and a classical subsystem. When the quantum subsystem is dynamically fast and the classical subsystem is slow, a vector potential is generated with a simple canonical transformation. This vector potential, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics; on the other hand, it yields a Lorentz-like force in the slow classical dynamics. In this way, the pure phase (Berry phase) of a wavefunction is linked to a physical force.

quant-ph↗
arXiv2005

Rational connectedness of log $Q$-Fano varieties

In this paper, we give an affirmative answer to a conjecture in the Minimal Model Program. We prove that log $Q$-Fano varieties of dim $n$ are rationally connected. We also study the behavior of the canonical bundles under projective morphisms.

math.AG↗
arXiv2003

Holomorphic forms on threefolds

Two conjectures relating the Kodaira dimension of a smooth projective variety and existence of number of nowhere vanishing 1-forms on the variety are proposed and verified in dimension 3.

math.AG↗