Exact Propagators for Soliton Potentials
Andrey M. Pupasov, Boris F. Samsonov
利用达布变换（或等价的超对称量子力学）方法，我们得到了具有多孤子势的一维薛定谔方程传播子的显式表达式.
Using the method of Darboux transformations (or equivalently supersymmetric quantum mechanics) we obtain an explicit expression for the propagator for the one-dimensional Schrödinger equation with a multi-soliton potential.
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Exact propagators for SUSY partners
研究了由通常的（线性）或多项式超对称相互关联的SUSY伙伴哈密顿算子对。假设其中一个哈密顿量的模型是已知传播子精确可解的，导出了伙伴模型的传播子表达式。相应的一般结果适用于“盒子中的粒子”、谐振子和自由粒子（即透明势）。
Time dependent Stark ladders: Exact propagator and caustic control
本文提出了一种新的粒子在含时场作用下在离散空间中的传播子。有了这个结果，我们就能够控制从点状源出现的焦散线的形状，因为波前的显式形式可以用外场来表示。
Exact propagators for atom-laser interactions
利用Laplace变换方法，得到了一类描述$N$能级原子与一组共共振$δ$激光相互作用的精确传播子.在强激光的极限中描述了状态选择镜。讨论了三能级原子的梯形、V形和$Λ$组态。对于两能级情形，研究了半无限长光束和波包与共振激光相互作用的瞬态效应。
Exact propagators for complex SUSY partners of real potentials
本文给出了一种计算实谱复势的精确传播子的方法，这些复势是实势的超对称伙伴。它说明了一些复杂的超对称合作伙伴的谐振子和零电位的传播子的例子。
There is no known exact expression for the propagator of a non-relativistic particle colliding with a hard sphere. De Prunelé (2008 {\it J.~Phys.~A:~Math.~Theor.} {\bf 41} 255305) derived a partial wave expansion of the propagator and compared it against some known approximations, including the semiclassical Van Vleck-Gutzwiller (VG) propagator; the VG propagator was evaluated entirely numerically. Here we point out that the VG propagator for the particle-sphere problem admits an analytic expression in terms of elementary functions.
Dynamics of quantum double dark-solitons and an exact finite-size scaling of Bose-Einstein condensation
本文研究一维玻色气体Lieb-Liniger模型中量子双暗孤子态的精确非平衡动力学，通过Bethe ansatz计算密度演化与宏观量子波函数，并给出基态BEC比例的精确有限尺寸标度，揭示准BEC在其中的关键作用。
On oscillator-bath system: Exact propagator, Reduced density matrix and Green's function
在Heisenberg图象下，得到了量子振子与由不同频率的$N$量子振子组成的玻色浴相互作用的量子传播子的精确形式.得到了振子的约化密度矩阵。得到了连接振子初始密度矩阵和任意时刻的密度矩阵的核或格林函数，并讨论了它与Feynman-Vernon影响泛函的关系.弱耦合制度和平方平均值的位置，动量和能量的振荡器得到平衡。
Closed-form propagator of the Calogero model
本文提出了Calogero模型传播子的精确闭式表达式，通过结合无谐振子势的本征函数关系公式及其多项式两体函数乘积有限和公式得出。
Exact propagators on the lattice with applications to diffractive effects
计算了离散薛定谔方程的传播子，并通过离散空间中的费曼路径求和揭示了其性质。利用这种新的传播算子，解析地研究了离散空间和连续时间中的衍射等初值问题。在本文的第二部分中，时间传播和一维障碍物的二维散射之间的类比进行了探讨。新的结果给出的背景下，衍射的边缘内的周期性介质。紧束缚阵列和光子晶体的连接表示。
We derive an exact quantum propagator for nonadiabatic dynamics in multi-state systems using the mapping variable representation, where classical-like Cartesian variables are used to represent both continuous nuclear degrees of freedom and discrete electronic states. The resulting expression is a Moyal series that, when suitably approximated, can allow for the use of classical dynamics to efficiently model large systems. We demonstrate that different truncations of the exact propagator lead to existing approximate semiclassical and mixed quantum-classical methods and we derive an associated er…
On the exactness of the Semi-Classical Approximation for Non-Relativistic One Dimensional Propagators
对于一维非相对论量子力学问题，我们研究了传播子的位置依赖性都在其相位中的条件，即半经典近似是精确的。对于速度无关势，我们发现：（i）势在空间上必须是二次的，但可以具有任意的时间依赖性。(ii)可以使相位与经典作用成比例，并且幅度（"波动因子“）也可以从经典解中找到。(iii)对于被驱动的谐振子，波动因子与驱动项无关。
In this paper we solve exactly the problem of the spectrum and Feynman propagator of a charged particle submitted to both an anharmonic oscillator in the plane and a constant and homogeneous magnetic field of arbitrary strength aligned with the perpendicular direction to the plane. As we shall see in the beginning of the letter the Hamiltonian, being a quadratic form, is easily diagonalizable and the Classical Action can be used to construct the exact Feynman Propagator using the Stationary Phase Approximation. The result is useful for the treatment of quasi two dimensional samples in the fiel…
Exact space-time propagator for the wave (second-order in time) equation in a layered system, made up of a layer sandwiched between two other different semi-infinite layers, is obtained by means of the multiple scattering theory (MST) approach. The wave equation for this layered system is characterized by the spatial dependence of the wave phase velocity which changes in the perpendicular-to-interfaces direction when crossing the interfaces and thus having different constant values in different layers of the threelayer. The MST approach is made possible due to obtained effective potentials loc…
We calculate infinite set of initial profiles of higher integer KdV solitons, which are both exactly solvable for the Schrodinger equation and for the Gel'fand-Levitan-Marchenko equation in the inverse scattering transform method of KdV equation. The calculation of these higher integer soliton solutions is based on the recently developed multi-indexed extensions of the reflectionless soliton potential.
Exact Bogoliubov-de Gennes Solutions for Grey Soliton Backgrounds
我们导出并讨论了一维Bogoliubov-de Gennes方程在三次非线性薛定谔方程的一般灰孤子解附近的小振幅激发下的完整精确解.我们的结果扩展了先前已知的静止暗孤子背景的情况。我们推导出我们的非零频率的解决方案，使用一个变种的薛定谔方程的无反射电位的因式分解方法。我们还详细讨论了零模解。
Starting from a total Lagrangian describing an oscillator-bath system, a novel derivation of exact quantum propagator is presented. Having the quantum propagator, the exact density matrix, reduced density matrix of the main oscillator and thermal equilibrium fixed point are obtained. The problem is generalised to the cases where the main oscillator is under the influence of a classical external force. By introducing generalised auxiliary classical fields, the generalised quantum propagator or generating functional of position correlation functions is obtained.
Exact coherent matter-wave soliton induced and controlled by laser field
利用具有振荡位置的高斯激光阱（势垒）来平衡原子间的排斥（吸引）相互作用，得到了囚禁在谐振势中的准一维玻色-爱因斯坦凝聚体（BEC）中相干亮孤子的一组精确解.明孤子在传输过程中不发生形变，并受到与俘获势共振的激光驱动的精确控制。排斥型BEC的孤子运动比吸引型BEC的稳定。结果表明，一种不同类型的孤子列车相比，最近在物理评论快报。100，164102（2008），并提出了一种产生和控制相干物质波孤子的实验方案。
We present a rigorous derivation of a semiclassical propagator for anticommuting (fermionic) degrees of freedom, starting from an exact representation in terms of Grassmann variables. As a key feature of our approach the anticommuting variables are integrated out exactly, and an exact path integral representation of the fermionic propagator in terms of commuting variables is constructed. Since our approach is not based on auxiliary (Hubbard-Stratonovich) fields, it surpasses the calculation of fermionic determinants yielding a standard form $\int {\cal D}[ψ,ψ^{*}] {\rm e}^{i R[ψ,ψ^{*}]}$ with …
Quasi exactly solvable quantum lattice solitons
本文利用一种新的相互作用推广了J.Dorignac等人最近研究的描述$f$量子振子的精确可解哈密顿量，并选择这种相互作用作为准精确可解的相互作用.研究了这种新的哈密顿量的谱的性质作为新的耦合常数的函数。这个哈密顿量和原来的哈密顿量也与适当的李结构有关。
Exact analytical soliton solutions in dipolar BEC
亮孤子、暗孤子和灰孤子是引力BEC和排斥BEC的Gross-Pitaevskii方程的著名孤子解。我们考虑完全极化粒子的偶极BEC中的孤子，说到偶极BEC，我们指的是磁化BEC和极化BEC。我们发现，这两种类型的偶极BEC揭示了不同的行为的集体激发。这与电场和磁场满足不同的麦克斯韦方程组有关。因此，我们独立地考虑它们。我们得到了精确的解析解的亮，暗，和灰色孤子在磁化（电极化）BEC时，他们传播平行和垂直于外磁（电）场。比较了两种偶极BEC的线性集体激发谱。
Quantum propagator for some classes of three-dimensional three-body systems
在这项工作中，我们解决了一类三体传播最一般的二次相互作用的坐标，任意的质量和耦合。这是通过使用Feynman路径积分形式主义对作为时间依赖耦合的常数和质量进行的。最后从传播子中恢复出能谱和本征函数。
Vector Representation of Exact Soliton Dynamics in Multi-component Nonlinear Schrödinger Systems
针对可积Manakov系统，提出一种矢量形式的Hirota双线性方法，直接在矢量层面处理耦合非线性薛定谔方程，统一描述亮、暗及混合孤子解及其非线性相互作用。
Feynman Propagator of the Arthurs-Kelly system at the Planck Scale
本文在Arthurs-Kelly系统中引入广义不确定性原理，精确推导出一阶GUP参数下的费曼传播子，并简要探讨其在早期宇宙中的应用。
We investigate bright solitons in the one-dimensional Schrödinger equation in the framework of an extended variational approach. We apply the latter to the stationary ground state of the system as well as to coherent collisions between two or more solitons. Using coupled Gaussian trial wave functions, we demonstrate that the variational approach is a powerful method to calculate the soliton dynamics. This method has the advantage that it is computationally faster compared to numerically exact grid calculations. In addition, it goes far beyond the capability of analytical ground state solutions…
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