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A fully resolvable quantum many-body Hamiltonian is introduced that mimics the behavior of the autocatalytic chemical reaction A+B <-> 2B involving two different molecular species, A and B. The model also describes two nonlinearly-coupled…
We study the closed Hamiltonian dynamics of a free particle moving on a ring, over one section of which it interacts linearly with a single harmonic oscillator. On the basis of numerical and analytical evidence, we conjecture that at small…
Using unitary transformations, we express the Kondo lattice Hamiltonian in terms of fermionic operators that annihilate the ground state of the interacting system and that represent the best possible approximations to the actual charged…
We introduce a new way to study molecular evolution within well-established Hamilton-Jacobi formalism, showing that for a broad class of fitness landscapes it is possible to derive dynamics analytically within the $1/N$-accuracy, where $N$…
The concept of out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness, using which one can study both chaotic and non-chaotic phenomena in the context of quantum statistical…
Deriving quantum error correction and quantum control from the Schrodinger equation for a unified qubit-environment Hamiltonian will give insights into how microscopic degrees of freedom affect the capability to control and correct quantum…
We present analytically exact results to show that, certain quasi one-dimensional lattices where the building blocks are arranged in a random fashion, can have an absolutely continuous part in the energy spectrum when special correlations…
We treat the ultraviolet problem for polaron-type models in nonrelativistic quantum field theory. Assuming that the dispersion relations of particles and the field have the same growth at infinity, we cover all subcritical…
We consider the Dicke Hamiltonian, a simple quantum-optical model which exhibits a zero-temperature quantum phase transition. We present numerical results demonstrating that at this transition the system changes from being quasi-integrable…
In ergodic quantum systems, physical observables have a non-relaxing component if they "overlap" with a conserved quantity. In interacting microscopic models, how to isolate the non-relaxing component is unclear. We compute exact dynamical…
Out-of-time-ordered correlators (OTOCs) have been extensively studied in recent years as a diagnostic of quantum information scrambling. In this paper, we study quantum information-theoretic aspects of the regularized finite-temperature…
Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…
Adaptive quantum circuits, in which unitary operations, measurements, and feedback are used to steer quantum many-body systems, provide an exciting opportunity to generate new dynamical steady states. We introduce an adaptive quantum…
Bose-Bose droplets are self-bound objects emerging from a mixture of two interacting Bose-Einstein condensates when their interactions are appropriately tuned. During droplet formation three continuous symmetries of the system's Hamiltonian…
In this paper the Hamiltonian of quantum electrodynamics with spatial cutoffs is investigated. We define a scaled total Hamiltonian and consider its asymptotic behavior. In the main theorem, it is shown that the scaled total Hamiltonian…
We study a pair of canonoid (fouled) Hamiltonians of the harmonic oscillator which provide, at the classical level, the same equation of motion as the conventional Hamiltonian. These Hamiltonians, say $K_{1}$ and $K_{2}$, result to be…
We consider a free quantum particle in one dimension whose mass profile exhibits jump discontinuities. The corresponding Hamiltonian is a self-adjoint realisation of the kinetic-energy operator, with the specific realisation determined by…
We clarify a few conceptual problems of quantum field theory on the level of exactly solvable models with fermions. The ultimate goal of our study is to gain a deeper understanding of differences between the usual ("spacelike") and…
Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and…
The wave functions corresponding to the zero energy eigenvalue of a one-dimensional quantum chain Hamiltonian can be written in a simple way using quadratic algebras. Hamiltonians describing stochastic processes have stationary states given…