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The theory of second order phase transitions is one of the foundations of modern statistical mechanics and condensed matter theory. A central concept is the observable `order parameter', whose non-zero average value characterizes one or…
A microscopic analysis of the superconducting quantum critical point realized via a pair-breaking quantum phase transition is presented. Finite temperature crossovers are derived for the electrical conductivity, which is a key probe of…
The statistics of gaps between quantum energy levels is a hallmark criterion in quantum chaos and quantum integrability studies. The relevant distributions corresponding to exactly integrable vs. fully chaotic systems are universal and…
Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum…
Nonequilibrium phase transitions are discussed with emphasis on general features such as the role of detailed balance violation in generating effective (long-range) interactions, the importance of dynamical anisotropies, the connection…
We consider electrons in a quantum wire interacting via a long-range Coulomb potential screened by a nearby gate. We focus on the quantum phase transition from a strictly one-dimensional to a quasi-one-dimensional electron liquid, that is…
Consider $D$ random systems that are modeled by independent $N\times N$ complex Hermitian Wigner matrices. Suppose they are lying on a circle and the neighboring systems interact with each other through a deterministic matrix $A$. We prove…
We investigate the critical behaviors of correlation length and critical exponents for strongly interacting bosons in a two-dimensional optical lattice via quantum Monte Carlo simulations. By comparing the full numerical results to those…
Atomic-like systems in which electronic motion is two dimensional are now realizable as ``quantum dots''. In place of the attraction of a nucleus there is a confining potential, usually assumed to be quadratic. Additionally, a perpendicular…
In this dissertation we use sophisticated numerical methods in order to examine ground-state (GS) properties of two types of quantum systems with electron electron interactions: A quantum dot (QD) and a nano-wire. In the first half of the…
Measurements of single electron tunneling through a quantum dot using a quantum point contact as charge detector have been performed for very long time traces with very large event counts. This large statistical basis is used for a detailed…
Quantum dots are small conducting devices containing up to several thousand electrons. We focus here on closed dots whose single-electron dynamics are mostly chaotic. The mesoscopic fluctuations of the conduction properties of such dots…
We review the use of an exact renormalization group equation in quantum field theory and statistical physics. It describes the dependence of the free energy on an infrared cutoff for the quantum or thermal fluctuations. Non-perturbative…
Quantum critical points are characterized by scale invariant correlations and correspondingly long ranged entanglement. As such, they present fascinating examples of quantum states of matter, the study of which has been an important theme…
A quantum phase transition is an unequivocal signature of strongly correlated many-body physics. Signatures of such phenomena are yet to be observed in ballistic transport through quantum wires. Recent developments in quantum wires have…
Coulomb blockade (CB) in a quantum dot (QD) with one anomalously broad level is considered. In this case many consecutive pronounced CB peaks correspond to occupation of one and the same broad level. Between the peaks the electron jumps…
We investigate the quantum phase transition of itinerant ferromagnets. It is shown that correlation effects in the underlying itinerant electron system lead to singularities in the order parameter field theory that result in an effective…
The contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a non-equilibrium phase transition into an absorbing state that has been widely investigated and shown to…
We consider the several phenomena which are taking place in Quantum Dots (QD) and Quantum Rings (QR): The connection of the Quantum Chaos (QC) with the reflection symmetry of the QD, Disappearance of the QC in the tunnel coupled chaotic QD,…
Metallic states near the Mott insulator show a variety of quantum phases including various magnetic, charge ordered states and high-temperature superconductivity in various transition metal oxides and organic solids. The emergence of a…