Related papers: Almost-zero-energy Eigenvalues of Some Broken Supe…
The prevalent role of force in traditional quantum mechanics is outlined, with special reference to approximate calculations for stationary states. It will be explored how far this force concept can be made useful in the concerned area. The…
We analyze the low-lying states for a one-dimensional potential consisting of $N$ identical wells, assuming that the wells are parabolic around the minima. Matching the exact wave functions around the minima and the WKB wave functions in…
Spontaneous symmetry breaking occurs in a system when its Hamiltonian possesses a certain symmetry, whereas the ground state wave functions do not preserve it. This provides such a scenario that a bifurcation, which breaks the symmetry,…
Under suitable assumptions, the quantum phase estimation (QPE) algorithm is able to achieve Heisenberg-limited precision scaling in estimating the ground state energy. However, QPE requires a large number of ancilla qubits and large circuit…
Considering recent advancements and successes in the development of efficient quantum algorithms for electronic structure calculations --- alongside impressive results using machine learning techniques for computation --- hybridizing…
The wavefunction of an incommensurate ground state for a one-dimensional discrete sine-Gordon model -- the Frenkel-Kontorova (FK) model -- at zero temperature is calculated by the quantum Monte Carlo method. It is found that the ground…
We calculate the energy spectrum of quasiparticles trapped by a domain wall separating different time reversal symmetry-breaking ground states in a hexagonal superconductor, such as UPt$_3$. The bound state energy is found to be strongly…
The energy spectra of mesoscopic, i.e. few-body quantum systems are of great interest in several areas of physics such as nuclear physics, cluster physics or magnetism. One way to obtain an approximate spectrum is to diagonalize with…
The total energy of the ground state of the quantum harmonic oscillator is obtained with minimal assumptions. The vacuum energy density of the universe is derived and a cutoff frequency is obtained for the upper bound of the quantum…
Today it still remains a challenge whether quantum mechanics has an underlying statistical explanation or not. While there are and were a lot of models trying to explain quantum phenomena with statistical methods these all failed on certain…
We propose a framework to construct the ground-state energy and density matrix of an N-electron system by solving selfconsistently a set of single-particle equations. The method can be viewed as a non-trivial extension of the Kohn-Sham…
We consider energetics and structural properties of a many particle system in one dimension with pairwise contact interactions confined in a parabolic external potential. To render the problem analytically solvable, we use the harmonic…
We present a simple and stable numerical method to approximate the ground state of a quantum many-body system by multiple determinant states. This method searches these determinant states one by one according to the matching pursuit…
We consider a class of ground states for quantum spin chains on an integer lattice. First we show that presence of the spectral gap between the ground state energy and the rest of spectrum implies the split property of certain subsystems.As…
We present a clear and mathematically simple procedure explaining spontaneous symmetry breaking in quantum mechanical systems. The procedure is applicable to a wide range of models and can be easily used to explain the existence of a…
The mechanism of electroweak symmetry breaking in Little Higgs Models is analyzed in an effective field theory approach. This enables us to identify observable effects irrespective of the specific structure and content of the heavy degrees…
We investigate the equilibration of an isolated macroscopic quantum system in the sense that deviations from a steady state become unmeasurably small for the overwhelming majority of times within any sufficiently large time interval. The…
A new Quasiparticle Random Phase Approximation approach is presented. The corresponding ground state is variationally determined and exhibits a minimum energy. New solutions for the ground state, some with spontaneously broken symmetry, of…
We study the ground state energy of a system of N fermions with two spin states in the large N limit. The particles are placed in an inhomogeneous trapping potential and interact via scaled interactions. We study a dilute limit where the…
The Principle of Naturalness of small parameters of a theory is reviewed. While quantum field theories constructed from gauge fields and fermions only are natural, those containing elementary scalar fields are not. In particular the Higgs…