Related papers: On the Phases of a Complex Matrix
We formulate and study a class of U(N)-invariant quantum mechanical models of large normal matrices with arbitrary rotation-invariant matrix potentials. We concentrate on the U(N) singlet sector of these models. In the particular case of…
Random matrix theory allows one to deduce the eigenvalue spectrum of a large matrix given only statistical information about its elements. Such results provide insight into what factors contribute to the stability of complex dynamical…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…
The hopping motion of classical particles on a chain coupled to reservoirs at both ends is studied for parallel dynamics with arbitrary probabilities. The stationary state is obtained in the form of an alternating matrix product. The…
We discuss correspondence between the predictions of quantum theories for rotation angle formulated in infinite and finite dimensional Hilbert spaces, taking as example, the calculation of matrix elements of phase-angular momentum…
This survey note describes a brief systemic view to approaches for evaluation of hierarchical composite (modular) systems. The list of considered issues involves the following: (i) basic assessment scales (quantitative scale, ordinal scale,…
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
Sign problems in path integrals arise when different field configurations contribute with different signs or phases. Phase unwrapping describes a family of signal processing techniques in which phase differences between elements of a time…
Phase transitions generically occur in random matrix models as the parameters in the joint probability distribution of the random variables are varied. They affect all main features of the theory and the interpretation of statistical models…
We consider matrix quantum mechanics with multiple bosonic matrices, including those obtained from dimensional reduction of Yang-Mills theories. Using the matrix bootstrap, we study simple observables like $\langle \mathop{tr} X^2 \rangle$…
We introduce a class of $n$-dimensional (possibly inhomogeneous) spin-like lattice systems presenting modulated phases with possibly different textures. Such systems can be parameterized according to the number of ground states, and can be…
This work is devoted to the study of discrete ambiguities. For parametrized potentials, they arise when the parameters are fitted to a finite number of phase-shifts. It generates phase equivalent potentials. Such equivalence was suggested…
This is a status report on a companion subject to extremal combinatorics, obtained by replacing extremality properties with emergent structure, `phases'. We discuss phases, and phase transitions, in large graphs and large permutations,…
In principle, the probability of configurations, determined by the system's partition function or wave function, encapsulates essential information about phases and phase transitions. Despite the exponentially large configuration space, we…
We have considered a disordered driven-diffusive system defined on a ring. This system can be mapped onto a heterogeneous zero-range process. We have shown that the grand-canonical partition function of this process can be obtained using a…
Systematic microcanonical inflection-point analysis of precise numerical results obtained in extensive generalized-ensemble Monte Carlo simulations reveals a bifurcation of the coil-globule transition line for polymers with a bending…
It is shown that the exponential moments of the canonical phase can be directly sampled from the data recorded in balanced homodyne detection. Analytical expressions for the sampling functions are derived, which are valid for arbitrary…
Defining, in the framework of quantum field theory, their mass eigenstates through their matricial propagator, we show why the mixing matrices of non-degenerate coupled systems should not be parametrized as unitary. This is how, for…
The critical behaviour of the $D=0$ matrix model with potential perturbed by nonlocal term generating touchings between random surfaces is studied. It is found that the phase diagram of the model has many features of the phase diagram of…