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In frustrated magnetic systems with a subextensive number of classical ground states, quantum zero-point fluctuations can select a unique long-range ordered state, a celebrated phenomenon referred to as \emph{order by quantum disorder}…
In this paper, we construct nonlinear coherent states for the generalized isotonic oscillator and study their non-classical properties in-detail. By transforming the deformed ladder operators suitably, which generate the quadratic algebra,…
In this paper, we study the quantum states generated from two and three linearly interacting quantum harmonic oscillators. We consider the possibility that one of the oscillators be under the influence of a classical external source and…
When the environment of an open quantum system is non-Markovian, amplitude and phase flow not only from the system into the environment but also back. Here we show that this feature can be exploited to carry out quantum control tasks that…
Motzkin chain is a model of nearest-neighbor interacting quantum $s=1$ spins with open boundary conditions. It is known that it has a unique ground state which can be viewed as a sum of Motzkin paths. We consider the case of periodic…
In the paper we developed a procedure for constructing generalized coherent states with shifted argument, as a result of the action of the generalized displacement operator. This was based on the action of a pair of nonlinear ladder…
Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables phi in R mod 2 pi and I > 0. But the symplectic transformation (\phi,I) to (q,p) is singular for (q,p) = (0,0). Globally {(q,p)} has…
Differential chains are a proper subspace of de Rham currents given as an inductive limit of Banach spaces endowed with a geometrically defined strong topology. Boundary is a continuous operator, as are operators that dualize to Hodge star,…
The goal of this note is to show that Jordan algebras and superalgebras provide an elegant and concise language for formulating quantum mechanical problems with inherent (super)conformal symmetry. The superconformal symmetries of the…
By the method of intense terahertz laser spectroscopy, we provide strong evidence that if an integer quantum Hall (IQH) system has asymmetric confining potential and the external quantizing magnetic field has a nonzero in-plane component,…
In this work we introduce discrete-time quantum walks in state space, more precisely on Fock-state lattices. Fock-state lattices provide a natural and clean setting for implementing lattice models, particularly in quantum optical systems.…
At second order in perturbation theory, we find the ground states of the $\phi^4$ double-well quantum field theory in 1+1 dimensions. The operators which create these ground states from the free vacuum are constructed explicitly at this…
Quantum ladder models, consisting of coupled chains, form intriguing systems bridging one and two dimensions and have been well studied in the context of quantum magnets and fermionic systems. Here we consider ladder systems made of more…
Bilayer quantum Hall system (BLQH) differ from its single layer counterparts (SLQH) by its symmetry breaking ground state and associated neutral gapless mode in the pseudo-spin sector. Due to the gapless mode, qualitatively good groundstate…
The ground state entanglement of the system, both in discrete-time and continuous-time cases, is quantified through the linear entropy. The result shows that the entanglement increases as the interaction between the particles increases in…
The unitary dynamics of isolated quantum systems does not allow a pure state to thermalize. Because of that, if an isolated quantum system equilibrates, it will do so to the predictions of the so-called "diagonal ensemble" $\rho_{DE}$.…
We consider the optimal approximation of certain quantum states of a harmonic oscillator with the superposition of a finite number of coherent states in phase space placed either on an ellipse or on a certain lattice. These scenarios are…
We study the coupled quantum Hall bilayers each at half-filled first excited Landau levels with varying the layer distance. Based on numerical exact diagonalization on torus, we identify two distinct phases separated by a critical layer…
In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schr\"{o}dinger equation by using the factorization method. The obtained generalized raising and lowering…
We explicitly construct and characterize all possible independent loop states in 3+1 dimensional loop quantum gravity by regulating it on a 3-d regular lattice in the Hamiltonian formalism. These loop states, characterized by the (dual)…