相关论文: One-parameter Darboux-transformed quantum actions …

In this paper we construct Darboux transformations for the supersymmetric Two-boson equation. Two Darboux transformations and associated B\"acklund transformations are presented. For one of them, we also obtain the corresponding the…

Quantum dots (QDs) are good model systems for fundamental studies of mesoscopic transport phenomena using thermoelectric effects because of their small size, electrostatically tunable properties and thermoelectric response characteristics…

Here, Darboux's classical results about transformations with differential substitutions for hyperbolic equations are extended to the case of parabolic equations of the form $L u = \big(D^2_{x} + a(x,y) D_x + b(x,y) D_y + c(x,y)\big)u=0$. We…

We briefly present the supersymmetric double Darboux method and next apply it to the continuum of the quantum Taub cosmological model as a toy model in order to generate a one-parameter family of bosonic Taub potentials and the…

Thermo Field Dynamics for inhomogeneous systems is generalized to quantum fields with a continuous single-particle mass spectrum. The modification of the hamiltonian in states with a local thermal Bogoliubov symmetry is used to calculate…

We develop a highly efficient method to numerically simulate thermal fluctuations and correlations in non-relativistic continuous bosonic one-dimensional systems. We start by noticing the equivalence of their description through the…

One-dimensional quantum systems admit duality relations that put hard core spinless bosons and fermions in one-to-one correspondence via Girardeau's mapping theorem. The simplest models of soft bosons interacting via zero-range potentials…

We generalize the formalism proposed by Dalibard, Dupont-Roc, and Cohen-Tannoudji [the DDC formalism] in the fourth order for two atoms in interaction with scalar fields in vacuum to a thermal bath at finite temperature $T$, and then…

From a given Fokker-Planck equation, a multi-parameter deformed partner Fokker-Planck equation is constructed. This is done by first deleting a set of eigenstates of the original FPE by the multi-step Darboux-Crum transformation, and then…

Algebraic Bargmann and Darboux transformations for equations of a more general form than the Schr\"odinger ones with an additional functional dependence h(r) in the right-hand side of equations are constructed. The suggested generalized…

We construct explicit Darboux transformations for a generalized, two-dimensional Dirac equation. Our results contain former findings for the one-dimensional, stationary Dirac equation, as well as for the fully time-dependent case in (1+1)…

The minimal set of thermodynamic control parameters consists of a statistical (thermal) and a mechanical one. These suffice to introduce all the pertinent thermodynamic variables; thermodynamic processes can then be defined as paths on this…

The Darboux transformation operator technique in differential and integral forms is applied to the generalized Schrodinger equation with a position-dependent effective mass and with linearly energy-dependent potentials. Intertwining…

We define thermodynamic configurations and identify two primitives of discrete quantum processes between configurations for which heat and work can be defined in a natural way. This allows us to uncover a general second law for any discrete…

The Darboux transformation operator technique is applied to construct exactly solvable anharmonic singular oscillator potentials and to study their coherent states. Classical system corresponding to a transformed quantum system is…

By solving the exact master equation of open quantum systems, we formulate the quantum thermodynamics from weak to strong couplings. The open quantum systems exchange matters, energies and information with their reservoirs through quantum…

Darboux transformation is constructed for superfields of the super sine-Gordon equation and the superfields of the associated linear problem. The Darboux transformation is shown to be related to the super B\"{a}cklund transformation and is…

We investigate the thermodynamic geometry of the quark-meson model at finite temperature, $T$, and quark number chemical potential, $\mu$. We extend previous works by the inclusion of fluctuations exploiting the functional renormalization…

We define and study the properties of Darboux-type transformations between Sturm--Liouville problems with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary…

We express Darboux transformations of discrete polarised curves as parallel sections of discrete connections in the quaternionic formalism. This immediately leads to the linearisation of the monodromy of the transformation. We also consider…