Related papers: Matrix model criticality and resonant tunneling
We consider the density of states of structured Hermitian random matrices with a variance profile. As the dimension tends to infinity the associated eigenvalue density can develop a singularity at the origin. The severity of this…
Recently it was argued that quantum phase transitions can be radically different from classical phase transitions with as a highlight the 'deconfined critical points' exhibiting fractionalization of quantum numbers due to Berry phase…
I review a variety of model systems and their quantum critical points, motivated by recent experimental and theoretical developments. These are used to present a general discussion of the non-zero temperature crossovers in the vicinity of a…
Experimentally there exist many materials with first-order phase transitions at finite temperature that display quantum criticality. Classically a strain-energy density coupling is known to drive first-order transitions in compressible…
We introduce a general method for transforming the equations of motion following from a Das-Jevicki-Sakita Hamiltonian, with boundary conditions, into a boundary value problem in one-dimensional quantum mechanics. For the particular case of…
We analyze further a recently proposed S-matrix description of transplanckian scattering in the specific case of axisymmetric collisions of extended sources, where some of the original approximations are not necessary. We confirm the claim…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
We analyze and overview several different unconventional quantum criticalities. One origin of the unconventionality is the proximity to first-order transitions. The border between the first-order and continuous transitions is described by a…
A rigorous understanding of brain dynamics and function requires a conceptual bridge between multiple levels of organization, including neural spiking and network-level population activity. Mounting evidence suggests that neural networks of…
A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of $\eta$-weak-pseudo-Hermitian position-dependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target…
We study a class of one-matrix models with an action containing nonpolynomial terms. By tuning the coupling constants in the action to criticality we obtain that the eigenvalue density vanishes as an arbitrary real power at the origin, thus…
On the phase diagram of a system undergoing a continuous phase transition of the second order, three lines, hyper-surfaces, convergent into the critical point feature prominently: the ordered and disordered phases in the thermodynamic…
We study a one-dimensional model which undergoes a transition between an active and an absorbing phase. Monte Carlo simulations supported by some additional arguments prompted as to predict the exact location of the critical point and…
We review some aspects of recent work concerning double scaling limits of singularly perturbed hermitian random matrix models and their connection to Painlev\'{e} equations. We present new results showing how a Painlev\'{e} III hierarchy…
Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian matrices are proposed. Moreover, an algorithm for computing…
This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in (sturm2003cones,huang2007complex,ai2011new). The enhanced property can be used to…
Quantum phase transitions arise in many-body systems due to competing interactions that promote rivaling ground states. Recent years have seen the identification of continuous quantum phase transitions, or quantum critical points, in a host…
Calculations for open quantum systems are performed usually by taking into account their embedding into one common environment, which is mostly the common continuum of scattering wavefunctions. Realistic quantum systems are coupled however…
We consider the two matrix model with an even quartic potential W(y)=y^4/4+alpha y^2/2 and an even polynomial potential V(x). The main result of the paper is the formulation of a vector equilibrium problem for the limiting mean density for…
We study local correlations of certain interacting particle systems on the real line which show repulsion similar to eigenvalues of random Hermitian matrices. Although the new particle system does not seem to have a natural spectral or…