Related papers: Quartic anharmonic many-body oscillator
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
We study the effects of anharmonicity on the physics of the Holstein model, which describes the coupling of itinerant fermions and localized quantum phonons, by introducing a quartic term in the phonon potential energy. We find that the…
Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding…
With the evolution of numerical methods, we are now aiming at not only qualitative understanding but also quantitative prediction and design of quantum many-body phenomena. As a novel numerical approach, machine learning techniques have…
The role of singular solutions in some simple quantum mechanical models is studied. The space of the states of two-dimensional quantum harmonic oscillator is shown to be separated into sets of states with different properties.
Response functions are key observables for probing the structure and dynamics of many-body systems. We introduce and demonstrate a quantum-classical framework for computing response functions of general many-fermion systems that also…
We present a systematic downfolding many-body approach for extended systems. Many-body calculations operate on a simpler Hamiltonian which retains material-specific properties. The Hamiltonian is systematically improvable and allows one to…
Dynamical instabilities can amplify small perturbations into measurable signals, offering a route to quantum-enhanced sensing. This mechanism was experimentally demonstrated in a collective-spin system with quadratic interactions, described…
We solve the model of N quantum Brownian oscillators linearly coupled to an environment of quantum oscillators at finite temperature, with no extra assumptions about the structure of the system-environment coupling. Using a compact…
This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum…
We describe the dynamics of many-body quantum chaotic systems at all time scales by studying the Green's and out-of-time order correlation (OTOC) functions of the four-body, $N$-Majorana Sachdev-Ye-Kitaev model. By combining the scramblon…
We propose a general strategy to develop quantum many-body approximations of primitives in linear algebra algorithms. As a practical example, we introduce a coupled-cluster inspired framework to produce approximate Hamiltonian moments, and…
Recovering trajectories of quantum systems whose classical counterparts display chaotic behavior has been a subject that has received a lot of interest over the last decade. However, most of these studies have focused on driven and…
Lectures notes for 2004 Les Houches Summer School on "Nanoscopic Quantum Transport". These lectures contain an introduction to Keldysh formalism for interacting bosonic and fermionic systems, presented in the functional integral framework.…
We have studied the underlying algebraic structure of the anharmonic oscillator by using the variational perturbation theory. To the first order of the variational perturbation, the Hamiltonian is found to be factorized into a…
The problem of the quantum harmonic oscillator is investigated in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero divisors. Starting with the commutator of the bicomplex position…
The quantum many-body problem lies at the center of the most important open challenges in condensed matter, quantum chemistry, atomic, nuclear, and high-energy physics. While quantum Monte Carlo, when applicable, remains the most powerful…
We use the quantum action to study the dynamics of quantum system at finite temperature. We construct the quantum action non-perturbatively and find temperature dependent action parameters. Here we apply the quantum action to study quantum…
Non-covalent interactions are a key ingredient to determine the structure, stability, and dynamics of materials, molecules, and biological complexes. However, accurately capturing these interactions is a complex quantum many-body problem,…
A shape invariant nonseparable and nondiagonalizable two-dimensional model with anharmonic complex interaction, first studied by Cannata, Ioffe, and Nishnianidze, is re-examined with the purpose of providing an algebraic construction of the…