Related papers: Modeling a quantum Hall system via elliptic equati…
Contrary to common belief, the current emitted by a contact embedded in a two-dimensional electron gas (2DEG) is quantized in the presence of electric and magnetic fields. This observation suggests a simple, clearly defined model for the…
In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this…
Dirac's method of classical analogy is employed to incorporate quantum degrees of freedom into modern nonequilibrium thermodynamics. The proposed formulation of dissipative quantum mechanics builds entirely upon the geometric structures…
This paper investigates the stabilization of a coupled system comprising a parabolic PDE and an elliptic PDE with nonlinear terms. A rigorous backstepping design provides an explicit boundary control law and exponentially convergent…
Coulomb coupled quantum dot arrays with staircase ground state configuration have been proposed in literature for enhancing heat-harvesting and refrigeration performance. However, due to their mutual Coulomb interaction, a performance…
Toroidal sigma models of magneto-transport are analyzed, in which integer and fractional quantum Hall effects automatically are unified by a {holomorphic modular symmetry}. By exploiting a quantum equivalence called \emph{mirror symmetry},…
Quantum simulators are controllable systems that can be used to simulate other quantum systems. Here we focus on the dynamics of a chain of molecular qubits with interposed antiferromagnetic dimers. We theoretically show that its dynamics…
Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear (gauge) transformation acting in the corresponding state space. The construction generalises a construction for nonlinear Schr\"odinger equations. To relate N^2…
It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…
We derive the equations of motion describing the feedback control of quantum systems in the regime of "good control", in which the control is sufficient to keep the system close to the desired state. One can view this regime as the quantum…
The helical Dirac states on the surface of a topological insulator are protected by topology and display significant particle-hole asymmetry. This asymmetry arises from a subdominant Schr\"{o}dinger type contribution to the Hamiltonian…
Nonlinearities in the dispersion relations associated with different interactions designs, boundary conditions and the existence of a physical cut-off scale can alter the quantum vacuum energy of a nonrelativistic system nontrivially. As a…
The fundamental question of how to best simulate quantum systems using conventional computational resources lies at the forefront of condensed matter and quantum computation. It impacts both our understanding of quantum materials and our…
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classical dynamics by combining ergodic theory with quantum…
Feedback control in open quantum dynamics is crucial for the advancement of various coherent platforms. However, currently only a handful of feedback master equations exist in the literature, which are restricted to specific types of…
This paper presents a realistic, stochastic, and local model that reproduces nonrelativistic quantum mechanics (QM) results without using its mathematical formulation. The proposed model only uses integer-valued quantities and operations on…
An improved hyperspherical harmonic method for the quantum three-body problem is presented to separate three rotational degrees of freedom completely from the internal ones. In this method, the Schr\"{o}dinger equation of three-body problem…
The paper deals with a cosmological model containing two scalar fields which can be considered as an extension of the Brans-Dicke scalar field model. Due to highly coupled non linear field equations, Noether Symmetry analysis has been…
In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the…
Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…