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The quantum phase transitions provide a paradigm for studying collective quantum phenomena that are a result of competing non-commuting interactions. This paper will study the ground state properties and quantum critical dynamics of the…
It is demonstrated that, if one remains in the framework of quantum mechanics taken alone, stationary states (energy eigenstates) are in no way singled out with respect to nonstationary ones, and moreover the stationary states would be…
The overlap measurement scheme accomplishes to evaluate the overlap of two input quantum states by only measuring an introduced auxiliary qubit, irrespective of the complexity of the two input states. We find a counterintuitive phenomenon…
Avoided crossings are fundamental phenomena in quantum mechanics and photonics that originate from the interaction between coupled energy levels and have been extensively studied in linear dispersive dynamics. Their manifestation in open,…
The phenomenon of the dark energy transition between the quintessence regime ($w > -1$) and the phantom regime ($w < -1$), also known as the cosmological constant boundary crossing, is analyzed in terms of the dark energy equation of state.…
Level repulsion is associated with exceptional points which are square root singularities of the energies as functions of a (complex) interaction parameter. This is also valid for resonance state energies. Using this concept it is argued…
Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…
Quantum resonance, i.e., amplification in transition probability available under certain conditions, offers a powerful means for determining fundamental quantities in physics, including the time duration of the second adopted in the SI…
Statistics of many particle energy levels of a finite two-dimensional system of interacting electrons is numerically studied. It is shown that the statistics of these levels undergoes a Poisson to Wigner crossover as the strength of the…
Resonance states of a two-electron quantum dot are studied using a variational expansion with both real basis-set functions and complex scaling methods. We present numerical evidence about the critical behavior of the density of states in…
Quantum theory for measurements of energy is introduced and its consequences for the average position of monitored dynamical systems are analyzed. It turns out that energy measurements lead to a localization of the expectation values of…
In the field of quantum chaos, the study of energy levels plays an important role. The aim of this review paper is to critically discuss some of the main contributions regarding the connection between classical dynamics, semi-classical…
Quantum phase transitions are sudden changes in the ground-state wavefunction of a many-body system that can occur as a control parameter such as a concentration or a field strength is varied. They are driven purely by the competition…
We study a disordered quantum solid incorporating two-level systems in which a group of atoms (or a single atom) can experience coherent tunnelling between two different positions and demonstrate that an effective mass deficit induced by…
The boundary modes of one dimensional quantum systems can play host to a variety of remarkable phenomena. They can be used to describe the physics of impurities in higher dimensional systems, such as the ubiquitous Kondo effect or can…
Experiments over the past years have demonstrated that it is possible to bring nanomechanical resonators and superconducting qubits close to the quantum regime and to measure their properties with an accuracy close to the Heisenberg…
Quantum phase transitions encompass a variety of phenomena that occur in quantum systems exhibiting several possible symmetries. Traditionally, these transitions are explored by continuously varying a control parameter that connects two…
A quantum model is considered for $N$ bosons populating two orthogonal single-particle modes with tunable energy separation in the presence of flavour-changing contact interaction. The quantum ground state is well approximated as a coherent…
The statistical properties of the dynamics of energy levels are investigated in the case of two two-dimensional disordered quantum dot models with nearest neighbor hopping subjected to external time-dependent perturbations. While in the…
Strong electron and spin correlations in a double-quantum-dot (DQD) can give rise to different quantum states. We observe a continuous transition from a Kondo state exhibiting a single-peak Kondo resonance to another exhibiting a double…