Related papers: On an exactly solvable toy model and its dynamics
We study a number of different ingredients related to the $\theta$ dependence, metastable excited vacuum states and other related subjects using a simplified version of QCD, the so-called "deformed QCD". This model is a weakly coupled gauge…
A new exactly solvable spatially one-dimensional quantum superradiance model describing a charged fermionic medium interacting with an external electromagnetic field is proposed. The infinite hierarchy of quantum conservation laws and…
Quantization of a toy model of a pseudointegrable Hamiltonian impact system is introduced, including EBK quantization conditions, a verification of Weyl's law, the study of their wavefunctions and a study of their energy levels properties.…
A new family of analytically solvable quantum geometric models is proposed. The structure of the energy spectra as well as the form of the corresponding eigenfunctions are presented pointing out their main specific properties.
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression…
The nonequilibrium dynamics of molecular devices is studied in the framework of a generic model for single-molecule transistors: a resonant level coupled by displacement to a single vibrational mode. In the limit of a broad level and in the…
Q-balls -- whether in the single-field or multi-field context -- are usually studied in theories containing only one stabilising symmetry. However, this is not the most general scenario. In this paper, we study a class of theories with…
Eigenvalues of eigenstates in jn configurations (n identical nucle- ons in the j -orbit) are functions of two-body energies. In some cases they are linear combinations of two-body energies whose coe+/-cients are independent of the…
I present the exact energy eigenstates and eigenvalues of a quantum many-body system of bosons on non-commutative space and in a harmonic oszillator confining potential at the selfdual point. I also argue that this exactly solvable system…
A key starting assumption in many classical interatomic potential models for materials is a site energy decomposition of the potential energy surface into contributions that only depend on a small neighbourhood. Under a natural stability…
We develop a constructive method to derive exactly solvable quantum mechanical models of rational (Calogero) and trigonometric (Sutherland) type. This method starts from a linear algebra problem: finding eigenvectors of triangular finite…
Incorporating time into thermodynamics allows addressing the tradeoff between efficiency and power. A qubit engine serves as a toy model to study this tradeoff from first principles, based on the quantum theory of open systems. We study the…
Even simplified models of quantum many-body systems can be difficult to analyse. However, taking inspiration from the foundations of physics, one may wonder whether there are practical advantages to constructing alternative beyond-quantum…
We show that a perturbed Coulomb problem discussed recently is conditionally solvable. We obtain the exact eigenvalues and eigenfunctions and compare the former with eigenvalues calculated by means of a numerical method. We discuss the…
We construct a toy model of a nucleon, in which three static quarks interact via a SU(3) gauge field on a planar honeycomb lattice. The dynamics of the gauge field is described by the Kogut-Susskind Hamiltonian, truncated to the lowest…
A one parameter solvable model for three bosons subject to delta function interactions in one-dimension with periodic boundary conditions is studied. The energy levels and wave functions are classified and given explicitly in terms of three…
We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science.…
In order to better understand quantum field theory we present some toy models on finite dimensional Hilbert spaces. We discuss how these models converge to a discrete spacetime version of quantum field theory. We first define toy fermion,…
We present a method which computes many-electron energies and eigenfunctions by a full configuration interaction which uses a basis of atomistic tight-binding wave functions. This approach captures electron correlation as well as atomistic…