Related papers: Optimized regulator for the quantized anharmonic o…
We study the effect of anharmonicity in quantum anharmonic oscillators, by computing the energy gap between the ground and the 1st excited state using the numerical bootstrap method. Based on perturbative formulae of limiting coupling…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
We aim to optimize the functional form of the compactly supported smooth (CSS) regulator within the functional renormalization group (RG), in the framework of bosonized two-dimensional Quantum Electrodynamics (QED_2) and of the…
In this article, the optimal control problem for a harmonic oscillator with an inequality constraint is considered. The applied energy of the oscillator during a fixed final time period is used as the performance criterion. The analytical…
In most cases, excited state quantum phase transitions can be associated with the existence of critical points (local extrema or saddle points) in a system's classical limit energy functional. However, an excited-state quantum phase…
We investigate the effects of dichotomous noise added to a classical harmonic oscillator in the form of stochastic time-dependent gain and loss states, whose durations are sampled from two distinct exponential waiting time distributions.…
By using the Feynman-Hibbs prescription for the evolution amplitude, we quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. The time-dependent quantum states of such a…
The gap between ground and first excited state of the quantum-mechanical double well is calculated using the Renormalization Group equations to the second order in the derivative expansion, obtained within a class of proper time regulators.…
Functional renormalization group methods formulated in the real-time formalism are applied to the $O(N)$ symmetric quantum anharmonic oscillator, considered as a $0+1$ dimensional quantum field-theoric model, in the next-to-leading order of…
We develop and analyze a new method for manipulation of energy in a quantum harmonic oscillator using coherent, e.g., electromagnetic, field and incoherent control. Coherent control is typically implemented by shaped laser pulse or tailored…
By using a previously established exact characterization of the ground state of random potential systems in the thermodynamic limit, we determine the ground and first excited energy levels of quantum random energy models, discrete and…
In this paper, we consider an anharmonic perturbation to the harmonic oscillator in the classical and the quantum regimes. We analyse a relativistic particle subjected to such a potential and then proceed to study a gas of such particles.…
We re-examine the well-studied one dimensional spin-1/2 $XY$ model to reveal its nontrivial energy spectrum, in particular the energy gap between the ground state and the first excited state. In the case of the isotropic $XY$ model -- the…
At one loop, quantum kinks are described by a sum of quantum harmonic oscillator Hamiltonians, and so their spectra are known exactly. We find the first correction beyond one loop to the quantum states corresponding to kinks with an excited…
We study the dynamics of a damped harmonic oscillator in the presence of a retarded potential with state-dependent time-delayed feedback. In the limit of small time-delays, we show that the oscillator is equivalent to a Li\'enard system.…
The energy levels of quantum systems are determined by quantization conditions. For one-dimensional anharmonic oscillators, one can transform the Schrodinger equation into a Riccati form, i.e., in terms of the logarithmic derivative of the…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
The efficient initialization of a quantum system is a prerequisite for quantum technological applications. Here we show that several classes of quantum states of a harmonic oscillator can be efficiently prepared by means of a…
The linear quadratic regulator is the fundamental problem of optimal control. Its state feedback version was set and solved in the early 1960s. However the static output feedback problem has no explicit-form solution. It is suggested to…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…