Di Yang
Integrability condition of Hamiltonian perturbations of integrable Hamiltonian PDEs of hydrodynamic type up to the second order approximation is considered.
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On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour
研究了最简双曲型方程$u_t + a(u) u_x=0$的Hamilton扰动.我们认为，扰动方程的解在未扰动方程的梯度突变点附近的行为应该基本上独立于一般扰动的选择，也不依赖于一般解的选择。此外，这种行为描述了一个特殊的解决方案，可积的四阶常微分方程。
Perturbation theory of PT-symmetric Hamiltonians
在微扰理论的框架下，利用稳定性技巧证明了一类$\PT$对称哈密顿算子的扰动特征值的真实性。我们将此方法应用于$\PT$对称未微扰哈密顿量受$\PT$对称附加相互作用的扰动。
The Chebotarev-Gregoratti Hamiltonian as singular perturbation of a nonsemibounded operator
通过将Albeverio-Kurasov构造的自伴扩张扩展到Fock空间，我们导出了与量子随机流相关联的哈密顿量。
On Effective Hamiltonians for Adiabatic Perturbations of Magnetic Schrodinger Operators
构造了磁Bloch带的几乎不变子空间和相应的有效哈密顿量。我们还讨论了与有效哈密顿量有关的动力学问题。我们假设磁势和电势分别是恒定磁场势和周期晶格势的缓慢变化的扰动。
Perturbation method for non-square Hamiltonians and its application to polynomial oscillators
本文对Rayleigh-Schroedinger微扰法作了一个显著的推广，它的（N+q）×（N+1）维哈密顿量（如新出现的，在束缚态的准精确构造期间）在q > 1处是非方阵。本征值的作用由能量/耦合q-小峰发挥。在所有阶中，其扰动通过q维反演来定义。
Numerical Evidence that the Perturbation Expansion for a Non-Hermitian $\mathcal{PT}$-Symmetric Hamiltonian is Stieltjes
最近，已经进行了几项具有$\mathcal{PT}$对称性的非厄米哈密顿量的研究。最引人注目的是，这些复杂的哈密顿是多么密切，他们的性质类似于那些传统的厄米哈密顿。本文提出了进一步的证据，这些哈密顿厄米哈密顿的相似性，通过检查的总和的$\mathcal{PT}$ -对称哈密顿$H=p^2+{1/4}x^2+iλx^3$的基态能量的发散弱耦合微扰级数最近研究的本德和邓恩。为此，计算了基态能量的瑞利-薛定谔微扰级数的前193个（非零）系数（以$λ^2$的幂表示）。Padé求和和Padé预测技术最近描述的Weniger应用到这个扰动序列。以这种方式获得的结果的定性特征是无法区分的情况下获得的四次非谐振子，这是已知的Stieltjes系列的微扰系列。
We consider metric perturbations of the Landau Hamiltonian. We investigate the asymptotic behaviour of the discrete spectrum of the perturbed operator near the Landau levels, for perturbations with power-like decay, exponential decay or compact support.
On the number of bound states for weak perturbations of spin-orbit Hamiltonians
对一类自旋轨道哈密顿量（包括Rashba和Dresselhaus哈密顿量）的弱扰动，给出了在连续谱下存在无穷多个束缚态的变分证明.
This work continues the study of the thermal Hamiltonian, initially proposed by J. M. Luttinger in 1964 as a model for the conduction of thermal currents in solids. The previous work [DL] contains a complete study of the "free" model in one spatial dimension along with a preliminary scattering result for convolution-type perturbations. This work complements the results obtained in [DL] by providing a detailed analysis of the perturbation theory for the one-dimensional thermal Hamiltonian. In more detail the following result are established: the regularity and decay properties for elements in t…
The Lie Transform Method for perturbations of contravariant antisymmetric tensor fields and its applications to Hamiltonian dynamics
借助于反变反对称张量场的Schouten演算，我们应用Lie变换方法研究了张量场的光滑变形，特别是由Poisson括号的变形产生的Hamilton系统的扰动.利用Karasev和Vorobiev关于泊松上同调计算的结果，我们描述了李变换的无穷小生成元。我们给出了六维李余代数上的扰动欧拉方程和配有狄拉克括号的泊松流形上的哈密顿系统的应用。
Dissipative Perturbations of 3d Hamiltonian Systems
本文给出了三维Hamilton系统自然耗散扰动的一些结果。给定一个哈密顿系统dx/dt = PdH，和一个Casimir函数S，我们构造一个对称协变张量g，使得修改的（所谓的“metriplectic”）系统dx/dt = PdH + gdS满足以下条件：dH是g的零向量，并且dS（gdS）< 0。沿着这种类型的动力系统的解，哈密顿函数H保持不变，而函数S减小，即S被系统耗散。我们的动机是由P. J. Morrison的松弛刚体的例子，其中引入了这种类型的系统。
This article investigates the stability of the ground state subspace of a canonical parent Hamiltonian of a Matrix product state against local perturbations. We prove that the spectral gap of such a Hamiltonian remains stable under weak local perturbations even in the thermodynamic limit, where the entire perturbation might not be bounded. Our discussion is based on preceding work by D.A. Yarotsky that develops a perturbation theory for relatively bounded quantum perturbation of classical Hamiltonians. We exploit a renormalization procedure, which on large scale transforms the parent Hamiltoni…
We propose a perturbation algorithm for Hamiltonian systems on a Lie algebra $\mathbb{V}$, so that it can be applied to non-canonical Hamiltonian systems. Given a Hamiltonian system that preserves a subalgebra $\mathbb{B}$ of $\mathbb{V}$, when we add a perturbation the subalgebra $\mathbb{B}$ will no longer be preserved. We show how to transform the perturbed dynamical system to preserve $\mathbb{B}$ up to terms quadratic in the perturbation. We apply this method to study the dynamics of a non-autonomous symmetric Rigid Body. In this example our algebraic transform plays the role of Iterative…
We study effects of perturbation Hamiltonian to quantum spin systems which can include quenched disorder. Model-independent inequalities are derived, using an additional artificial disordered perturbation. These inequalities enable us to prove that the variance of the perturbation Hamiltonian density vanishes in the infinite volume limit even if the artificial perturbation is switched off. This theorem is applied to spontaneous symmetry breaking phenomena in a disordered classical spin model, a quantum spin model without disorder and a disordered quantum spin model.
We study solutions of the functional eigenstate equation of a free quantum field Hamiltonian. Admissible solutions are to have a finite norm and a finite eigenvalue w.r.t. the norm and eigenvalue of the ground state of the free theory. We show that in the simple cases of a scalar field and of a vector field in the Coulomb gauge the admissible eigenstates exist and possess negative energy. The functionals can be treated as infinite-dimensional counterparts of the eigenfunctions of the theory of singular perturbations of differential operators, and can be deployed for construction of the renorma…
Renormalization of bosonic quadratic Hamiltonians involving rank-one perturbations
该研究通过玻利约夫转换对包含一阶扰动的玻色二次哈密顿量进行重整化，探讨了不同重整化方法对能量和耦合常数的影响。
Our main goal in this paper is to prove existence (and uniqueness) of the quantum propagator for time dependent quantum Hamiltonians $\hat H(t)$ when this Hamiltonian is perturbed with a quadratic white noise $\dotβ\hat K$. $β$ is a continuous function in time $t$, $\dot β$ its time derivative and $K$ is a quadratic Hamiltonian. $\hat K$ is the Weyl quantization of $K$. For time dependent quadratic Hamiltonians $H(t)$ we recover, under less restrictive assumptions, the results obtained in \cite{bofu, du}.In our approach we use an exact Hermann Kluk formula \cite{ro2} to deduce a Strichartz est…
On applying the subspace perturbation theory to few-body Hamiltonians
我们提出了一个选择的结果厄米特算子的谱子空间的厄米特扰动下的变化，并显示这些结果可能会工作的少体哈密顿。
We consider the fractional powers of singular (point-like) perturbations of the Laplacian, and the singular perturbations of fractional powers of the Laplacian, and we compare such two constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators we outline a programme of relevant questions that deserve being investigated.
A note on the KAM theorem for partially integrable Hamiltonian systems
本文给出了部分可积哈密顿系统到完全可积系统的辛约化。KAM定理被应用到这个约化的完全可积的哈密顿系统。它的KAM扰动产生了原来的部分可积系统的扰动，使得由这个扰动保持的环面集是大的。
The nonlinear Vlasov equation contains the full nonlinear dynamics and collective effects of a given Hamiltonian system. The linearized approximation is not valid for a variety of interesting systems, nor is it simple to extend to higher order. It is also well-known that the linearized approximation to the Vlasov equation is invalid for long times, due to its inability to correctly capture fine phase space structures. We derive a perturbation theory for the Vlasov equation based on the underlying Hamiltonian structure of the phase space evolution. We obtain an explicit perturbation series for …
Non-Random Perturbations of the Anderson Hamiltonian in the 1-D case
最近（参见Molchanov & Vainberg 2011），两位作者将Lieb方法应用于研究$H=H_0-W$形式的特定算子的负谱。这里，$H_0$是正随机（或子随机）半群的生成元，$W(x) \geq 0$和$W(x) \to 0$是某个相空间$X$上的$x \to \infty$。他们在几种“奇异”情况下使用了一般结果，其中包括安德森哈密顿量$H_0$。在1维的情况下，本论文的主题，我们将证明类似的，但更精确的结果。
Pure Point Spectrum of the Floquet Hamiltonian for the Quantum Harmonic Oscillator Under Time Quasi- Periodic Perturbations
我们证明了$1-d$量子谐振子在空间定域、时间准周期扰动下对正测度丢番图频率是稳定的。这证明了Enss-Veselic在他们1983年的论文\cite{EV}中提出的一个猜想。本文的动机也来自于相应的非线性方程的拟周期解的构造。
On Hamiltonian perturbations of hyperbolic systems of conservation laws
本文研究了一维空间双曲型偏微分方程组哈密顿扰动形式扰动解的一般结构。在一定的一般性假设下，证明了任何双哈密顿扰动都可以通过改变无限喷流空间上的坐标来消除扰动展开的所有阶数，该坐标合理地依赖于导数。主要的工具是在建设所谓的准三浦变换射流坐标消除任意变形的半简单bihamilton结构的流体动力学类型（准平凡性定理）。我们还描述，以下\cite{LZ1}，这样的双哈密顿结构的不变量相对于组的三浦型变换多项式依赖于衍生物。
Motivated by applications of the discrete random Schrödinger operator, mathematical physicists and analysts, began studying more general Anderson-type Hamiltonians; that is, the family of self-adjoint operators $$H_ω= H + V_ω$$ on a separable Hilbert space $\mathcal{H}$, where the perturbation is given by $$V_ω= \sum_n ω_n (\cdot, φ_n)φ_n$$ with a sequence $\{φ_n\}\subset\mathcal{H}$ and independent identically distributed random variables $ω_n$. We show that the the essential parts of Hamiltonians associated to any two realizations of the random variable are (almost surely) related by a rank …
We consider the asymptotic behavior of the spectrum of the Landau Hamiltonian plus a rapidly decaying potential, as the magnetic field strength, $B$, tends to infinity. After a suitable rescaling, this becomes a semiclassical problem where the role of Planck's constant is played by $1/B$. The spectrum of the operator forms eigenvalue clusters. We obtain a Szegő limit theorem for the eigenvalues in the clusters as a suitable cluster index and $B$ tend to infinity with a fixed ratio $\calE$. The answer involves the averages of the potential over circles of radius $\sqrt{\calE/2}$ (circular Radon…
Non-random perturbations of the Anderson Hamiltonian
考虑Anderson哈密顿量$H_0=-Δ+V(x,ω)$，其中$V$为Bernoulli型随机势.算子$H_0$受非随机连续势$-w(x) \leq 0$的扰动，在无穷远处衰减。它将表明，之间的边界线，和无穷多个负特征值的扰动运营商，是实现与潜在的$-w(x)$衰减为$O(\ln^{-2/d} |x|)$。
The Riemann-Hilbert approach to obtain critical asymptotics for Hamiltonian perturbations of hyperbolic and elliptic systems
本文综述了双曲型和椭圆型偏微分方程组Hamilton扰动临界性态描述的最新进展。有人指出，这种行为可以描述的杰出Painlevé超越，这是普遍的意义上说，他们是，在某种程度上，独立的方程和初始数据。我们将考虑几个著名的可积方程的例子，这些方程在临界点附近会表现出这种类型的Painlevé行为。Riemann-Hilbert方法是一个有用的工具，以获得严格的结果，这样的方程。我们将解释这种方法的主线，我们将讨论的普遍性猜想从黎曼-希尔伯特的观点。
It is shown that the variance of a perturbation Hamiltonian density vanishes in the infinite-volume limit of the perturbed spin systems with quenched disorder. This is proven in a simpler way and under less assumptions than before. A corollary of this theorem indicates the impossibility of non-spontaneous replica symmetry-breaking in disordered spin systems. The commutativity between the infinite-volume limit and the switched-off limit of a replica symmetry-breaking perturbation implies that the variance of the spin overlap vanishes in the replica symmetric Gibbs state.
This work explores a structure of the Deprit perturbation series and its connection to a Kato resolvent expansion. It extends the formalism previously developed for the Hamiltonians linearly dependent on perturbation parameter to a nonlinear case. We construct a canonical intertwining of perturbed and unperturbed averaging operators. This leads to an explicit expression for the generator of the Lie-Deprit transform in any perturbation order. Using this expression, we discuss a regular pattern in the series, non-uniqueness of the generator and normalised Hamiltonian, and the uniqueness of the G…
Spectral Analysis of a Two Body Problem with Zero Range Perturbation
本文考虑了由一个测试粒子和一个谐振子组成的一维、二维和三维量子系统的哈密顿量的一类奇异零程扰动，并研究了它的谱。事实上，我们给出了点谱的详细特征及其关于进入哈密顿量的参数的渐近行为。我们还部分描述了哈密顿量的正谱和散射性质。
Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions
我们展示了如何将具有束缚强度k体相互作用的给定n量子位目标哈密顿映射到具有两体相互作用的模拟器哈密顿上，使得目标和模拟器哈密顿的基态能量相同，对于任意小的π，误差为O（π n）。模拟器哈密顿量中的相互作用强度取决于k和k，但不取决于n。我们完成这一减少使用一种新的方法来推导一个有效的低能量哈密顿量，依赖于多体物理的Schriffal-Wolff变换。
Variational principle for Hamiltonians with degenerate bottom
我们考虑扰动的哈密顿的傅立叶符号达到其最小值沿超曲面。这样的算子出现在几个领域，如自旋电子学，超导电性理论，或超流理论。下面的本质谱的扰动潜力的特征值的数目的变分估计。特别是，我们提供了一个初步的证明，负电位导致一个无限的离散谱。
Integrable perturbations of polynomial Hamiltonian systems
研究在原点非退化平衡位置的哈密顿系统，通过非共振假设证明存在解析函数F，使H+F在R^{2n}中完全可积。
Lower-dimensional invariant tori for perturbations of a class of non-convex Hamiltonian functions
考虑一类准可积哈密顿系统，该系统是通过向可积系统的非凸哈灵顿函数添加仅取决于角度变量的扰动而获得的。我们专注于一个共振的极大环面的未扰动系统，叶成一个家庭的低维环面余维1，不变的准周期流的旋转向量满足一些温和的丢番图条件。我们表明，至少有一个低维环面的旋转矢量总是存在的扰动系统。证明是基于发散级数的多尺度分析和重算程序。一个关键的作用是发挥适当的对称性和取消，最终由于系统的哈密顿结构。
Spectral edge regularity of magnetic Hamiltonians
我们分析了谱边正则性的一大类磁哈密顿时产生的扰动是由一个全球有界的磁场。我们可以证明谱边的Lipschitz正则性，无论磁场扰动是常数还是缓变。我们还恢复了G. Nenciu谁证明Lipschitz正则性的对数因子一般全球有界磁场扰动。
We study random Hamiltonians on finite-size cubes and waveguide segments of increasing diameter. The number of random parameters determining the operator is proportional to the volume of the cube. In the asymptotic regime where the cube size, and consequently the number of parameters as well, tends to infinity, we derive deterministic and probabilistic variational bounds on the lowest eigenvalue, i.e. the spectral minimum, as well as exponential off-diagonal decay of the Green function at energies above, but close to the overall spectral bottom.
Integrable Hamiltonian systems on almost-symplectic manifolds have recently drawn some attention. Under suitable properties, they have a structure analogous to those of standard symplectic-Hamiltonian completely integrable systems. Here we study small Hamiltonian perturbations of these systems. Preliminarily, we investigate some general properties of these systems. In particular, we show that if the perturbation is `strongly Hamiltonian' (namely, its Hamiltonian vector field is also a symmetry of the almost-Hamiltonian structure) then the system reduces, under an almost-symplectic version of s…
The non-local quantum field theories attract interest in the mathematical and physical community as candidates for effective description of the reality taking into account the quantum gravity effects. The standard methods, developed for the conventional local quantum field theories, often are not applicable. In this paper the Hamiltonian approach, originally proposed for quantization of the non-local effective theory inspired by non-commutative geometry of the Doplicher-Fredenhagen-Roberts Quantum Spacetime, is generalized to a large class of ultraviolet finite non-local Hamiltonian perturbati…
In this paper, we explore the stability of the energy landscape of an Ising Hamiltonian when subjected to two kinds of perturbations: a perturbation on the coupling coefficients and external fields, and a perturbation on the underlying graph structure. We give sufficient conditions so that the ground states of a given Hamiltonian are stable under perturbations of the first kind in terms of order preservation. Here by order preservation we mean that the ordering of energy corresponding to two spin configurations in a perturbed Hamiltonian will be preserved in the original Hamiltonian up to a gi…
In this paper we prove a Nekhoroshev type theorem for perturbations of Hamiltonians describing a particle subject to the force due to a central potential. Precisely, we prove that under an explicit condition on the potential, the Hamiltonian of the central motion is quasi-convex. Thus, when it is perturbed, two actions (the modulus of the total angular momentum and the action of the reduced radial system) are approximately conserved for times which are exponentially long with the inverse of the perturbation parameter.
Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models
研究了一类多通道量子力学模型--描述粒子与局域自旋相互作用的哈密顿量在$d=1,2,3$维中的本征值和共振态的扰动.我们考虑未扰动哈密顿量在连续谱的阈值处显示本征值和共振，并分析了各种类型的扰动对谱奇异性的影响。我们提供的算法，以获得收敛的级数展开的坐标的奇点。
Homoclinic Tubes in Discrete Nonlinear Schroedinger Equation Under Hamiltonian Perturbations
本文研究了离散立方非线性薛定谔晶格在哈密顿扰动下的性质。首先，我们发展了一个完整的等谱理论的双曲结构的晶格无微扰。特别地，利用Backlund-Darboux变换来生成异宿轨道和Melnikov向量。然后给出了扰动格点的持久不变流形和Fenichel纤维的坐标表达式。最后，基于上述机制，通过Melnikov型计算和隐函数论证，证明了余维2横截同宿管的存在性.我们还讨论了符号动力学的不变管，其中每一个由一个双无穷序列的曲线段时，晶格是四维的。研究了横截同宿管的渐近流形内部的结构，研究了四维格点的特殊轨道，特别是同宿轨道和异宿轨道。
In [2] it has been proved that a linear Hamiltonian lattice field perturbed by a conservative stochastic noise belongs to the 3/2-Lévy/Diffusive universality class in the nonlinear fluctuating theory terminology [15], i.e. energy superdiffuses like an asymmetric stable 3/2-Lévy process and volume like a Brownian motion. According to this theory this should remain valid at zero tension if the harmonic potential is replaced by an even potential. In this work we consider a quartic anharmonicity and show that the result obtained in the harmonic case persists up to some small critical value of the …
The present study is the first such attempt to examine rigorously and comprehensively the spectral properties of a three-dimensional ultracold atom when both the spin-orbit interaction and the Zeeman field are taken into account. The model operator is the Rashba spin-orbit coupled operator in dimension three. The self-adjoint extensions are constructed using the theory of singular perturbations, where regularized rank two perturbations describe spin-dependent contact interactions. The spectrum of self-adjoint extensions is investigated in detail laying emphasis on the effects due to spin-orbit…
Explicit Calculations for Anharmonic Oscillators Using Lie Algebras
我们构造了由调和哈密顿量和扰动非调和哈密顿量的扩张子产生的李代数。从那里，我们形成一个非常具体的元素的相关李群和变换的未扰动的哈密顿量到扰动的哈密顿量减去扰动能量。给出了所有形式为H = a^{ \dagger }a + 1/2 + λx^n的哈密顿量的一阶微扰能量的显式表达式.
A Trace Formula for Long-Range Perturbations of the Landau Hamiltonian
我们考虑长程电势$V$扰动下的朗道哈密顿量。扰动算子的谱由特征值簇组成，这些特征值簇累积到朗道能级。首先，我们得到了估计的收缩率，这些集群的朗道水平的集群$q$的数量趋于无穷大。进一步，我们假设存在一个适当的$\V$，齐次的顺序$-ρ$与$ρ\in (0,1)$，使$V(x) = \V(x) + O(|x|^{-ρ- ε})$，$ε> 0$，作为$|x| \to \infty$，并调查的渐近分布的特征值在一个给定的集群，作为$q \to \infty$。我们得到一个明确的描述的渐近密度的特征值的平均值变换的$\V$。
Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory
在第一部分中，我们提出了一个介绍多辛形式主义，这是概括的汉密尔顿的制定力学的变分法与多个变量：我们给出了一些物理动机，有关的量子场论，并阐述了最简单的例子，理论的基础上，由于T。de Donder和H.外尔在第二部分，我们解释迅速合作的工作J. Kouneiher（math-ph/0211046）的推广德Donder-Weyl理论（称为Lepage理论）。最后，我们表明，在这个框架下，微扰经典场论（模拟微扰量子场论）可以构建。
We consider a mechanical system consisting of $n$ penduli and a $d$-dimensional generalized rotator subject to a time-dependent perturbation. The perturbation is not assumed to be either Hamiltonian, or periodic or quasi-periodic. The strength of the perturbation is given by a parameter $ε\in\mathbb{R}$. For all $|ε|$ sufficiently small, the augmented flow has a $(2d + 1)$-dimensional normally hyperbolic locally invariant manifold $\tildeΛ_ε$. We define a Melnikov vector, which gives the first order expansion of the displacement of the stable and unstable manifolds of $\tildeΛ_0$ under the per…
Perturbation of an eigenvalue from a dense point spectrum: a general Floquet Hamiltonian
考虑Hilbert空间$L^2([0,T],E,dt)$中的扰动Floquet Hamilton算子$-i\partial_t + H + βV(ωt)$.这里$H$是$E$中的自伴算子，其离散谱服从增长间隙条件，$V(t)$是$E$中的对称有界算子，其依赖于$t$ $2π$ -周期性地，$ω= 2π/T$是频率，$β$是耦合常数。对于几乎所有的$ω$，未扰动部分的谱$Spec(-i\partial_t + H)$是纯点的，并且在$R$中是稠密的。这一事实排除了正则微扰理论的应用。然而，我们表明，几乎所有的$ω$和提供$V(t)$是足够光滑的，微扰理论仍然是有意义的，但是，有两个修改。首先，耦合常数被限制到一个集合$I$，它不需要是一个区间，但0仍然是$I$的密度点。第二，瑞利-薛定谔级数对扰动本征值和扰动本征向量是渐近的。
Topological quantum order: stability under local perturbations
本文研究了在与时间无关的弱扰动下物质拓扑相的零温稳定性。我们的结果适用于量子自旋哈密顿量，可以写为一个数字的几何本地交换投影仪的D维晶格具有一定的拓扑顺序条件。对于这样的哈密顿量H_0，我们证明了存在一个常数阈值ε>0，使得对于任何可表示为短程有界范数相互作用之和的扰动V，扰动哈密顿量H=H_0+εV具有定义明确的谱带，这些谱带起源于H_0的O（1）个最小本征值。这些带与光谱的其余部分分开，并且彼此之间有一个恒定的间隙。起源于H_0的最小本征值的能带具有指数小的宽度（作为晶格尺寸的函数）。我们的证明利用离散版本的哈密顿流方程，相对有界算子的理论，和Lieb-Robinson界。
Usage of a Hamiltonian perturbation theory for a nonconservative system is counterintuitive and in general, a technical impossibility by definition. However, the time-independent dual Hamiltonian formalism for the nonconservative systems have opened the door for using various conservative perturbation theories for investigating the dynamics of such systems. Here we demonstrate that the Lie transform Hamiltonian perturbation theory can be adapted to find the perturbative solutions and the frequency corrections for the dissipative oscillatory systems. As a further application, we use the perturb…
In this paper we study up to which extent we can apply adiabatic control strategies to a quantum control model obtained by rotating wave approximation. In particular, we show that, under suitable assumptions on the asymptotic regime between the parameters characterizing the rotating wave and the adiabatic approximations, the induced flow converges to the one obtained by considering the two approximations separately and by combining them formally in cascade. As a consequence, we propose explicit control laws which can be used to induce desired populations transfers, robustly with respect to par…
Invariant states of linear quantum stochastic systems under Weyl perturbations of the Hamiltonian and coupling operators
研究线性量子随机系统在非线性扰动下的不变态敏感性，利用Weyl量化形式分析哈密顿量和耦合算符的扰动，探讨空间频率域中不变态的修正应用。
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