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Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…
We explore the theory of electrons confined by one dimensional power law potentials. We calculate the density profile in the high density electron gas, the low density Wigner crystal, and the intermediate regime. We extract the momentum…
A new super-symmetric representation for quantum disordered systems is derived. This representation is exact and is dual to that of the nonlinear sigma-model. The new formalism is tested by calculating the distribution of wave function…
Following two recent papers [Phys. Chem. Chem. Phys. 2015, \textbf{17}, 3196; Mol. Phys. 2015, \textbf{113}, 1843], we perform a larger-scale study of chemical structure in one dimension (1D). We identify a wide, and occasionally…
From a careful study of the transcendental equations fulfilled by the bound state energies of a free particle in a quantum well, cylindrical wire or spherical dot with finite potential barrier, we have derived analytical expressions of…
The phase structure of QCD remains an open fundamental problem of standard model physics. In particular at finite density, our knowledge is limited. Yet, numerous model studies point towards a rich and complex phase diagram at large…
Using the Landauer formulation of transport theory, we predict that dielectric quantum wires should exhibit quantized thermal conductance at low temperatures in a ballistic phonon regime. The quantum of thermal conductance is universal,…
The low temperature phase diagram of 1D disordered quantum systems like charge or spin density waves, superfluids and related systems is considered by a full finite T renormalization group approach, presented here for the first time. At…
We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the…
The energy spectrum and corresponding wave functions of a flat quantum dot with elliptic symmetry are obtained exactly. A detailed study is made of the effect of ellipticity on the energy levels and the corresponding wave functions. The…
The density of states of one-dimensional disordered electron systems with long range Coulomb interaction is studied in the weak pinning limit. The density of states is found to follow a power law with an exponent determined by localization…
We derive fundamental bounds for general quantum metrological models involving both temporal or spatial correlations (mathematically described by quantum combs), which may be effectively computed in the limit of a large number of probes or…
In this brief tutorial review, I show how phase coherent properties of disordered conductors can be described in a simple and unified way. These properties include transport properties like weak-localization correction and universal…
The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary…
Using the basic ingredient of supersymmetry, we develop a simple alternative approach to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wave functions do not involve tedious…
The physical aspect of a general perturbation theory is explored. Its role as a physical principle for understanding the interaction among the matters with different levels of hierarchy is appreciated. It is shown that the general…
What does it mean for one quantum process to be more disordered than another? Here we provide a precise answer to this question in terms of a quantum-mechanical generalization of majorization. The framework admits a complete description in…
We study the thermodynamics of various physical systems in the framework of the Generalized Uncertainty Principle that implies a minimal length uncertainty proportional to the Planck length. We present a general scheme to analytically…
The minimal set of thermodynamic control parameters consists of a statistical (thermal) and a mechanical one. These suffice to introduce all the pertinent thermodynamic variables; thermodynamic processes can then be defined as paths on this…