Related papers: Effective Hamiltonian with holomorphic variables
A universal algorithm to construct N-particle (classical and quantum) completely integrable Hamiltonian systems from representations of coalgebras with Casimir element is presented. In particular, this construction shows that quantum…
In general relativity, the Einstein equations provide spherically symmetric static spacetimes with dynamics defined as an evolution along the radial coordinate $r$. The geometrical sector becomes a one-dimensional mechanical system, with…
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few…
Most classical mechanical systems are based on dynamical variables whose values are real numbers. Energy conservation is then guaranteed if the dynamical equations are phrased in terms of a Hamiltonian function, which then leads to…
We offer a new Hamiltonian formulation of the classical Pais-Uhlenbeck Oscillator and consider its canonical quantization. We show that for the non-degenerate case where the frequencies differ, the quantum Hamiltonian operator is a…
We present a straightforward method for obtaining exact classical and quantum molecular Hamiltonians in terms of arbitrary coordinates. As compared to other approaches the resulting expression are rather compact, the physical meaning of…
This paper investigates the thermodynamics of a large class of non-Hermitian, $PT$-symmetric oscillators, whose energy spectrum is entirely real. The spectrum is estimated by second-order WKB approximation, which turns out to be very…
The dynamics of the spin-boson Hamiltonian is considered in the stochastic approximation. The Hamiltonian describes a two-level system coupled to an environment and is widely used in physics, chemistry and the theory of quantum measurement.…
A quantum realization of the Relativistic Harmonic Oscillator is realized in terms of the spatial variable $x$ and ${\d\over \d x}$ (the minimal canonical representation). The eigenstates of the Hamiltonian operator are found (at lower…
The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof is given to establish the physical…
Time dependent quadratic Hamiltonians are well known as well in classical mechanics and in quantum mechanics. In particular for them the correspondance between classical and quantum mechanics is exact. But explicit formulas are non trivial…
With our recently proposed effective Hamiltonian via Monte Carlo, we are able to compute low energy physics of quantum systems. The advantage is that we can obtain not only the spectrum of ground and excited states, but also wave functions.…
We propose a general variational fermionic many-body wavefunction that generates an effective Hamiltonian in a quadratic form, which can then be exactly solved. The theory can be constructed within the density functional theory framework,…
Optimal measurement is required to obtain the quantum and classical correlations of a quantum state, and the crucial difficulty is how to acquire the maximal information about one system by measuring the other part; in other words, getting…
In this paper the old problem of determining the discrete spectrum of a multi-particle Hamiltonian is reconsidered. The aim is to bring a fermionic Hamiltonian for large numbers N of particles by analytical means into a shape such that…
The problem of finding superintegrable Hamiltonians and their integrals of motion can be reduced to solving a series of compatibility equations that result from the overdetermination of the commutator or Poisson bracket relations. The…
The framework of the Perturbed Static Path Approximation (PSPA) is used to calculate the partition function of a finite Fermi system from a Hamiltonian with a separable two body interaction. Therein, the collective degree of freedom is…
In the paper we describe the modification of self-consistent harmonic approximation for quantum S=1 systems. This method has a number of advantages in comparison with usual SCHA. We apply the method to two-dimensional ferromagnets with…
Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schr\"odinger equation are at the heart of computational materials science. In that respect the coupled cluster hierarchy of methods plays a…
Recently, variational quantum metrology was proposed for Hamiltonians with multiplicative parameters, wherein the estimation precision can be optimized via variational circuits. However, systems with generic Hamiltonians still lack these…