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Miloslav Znojil - One of the best experts on this subject based on the ideXlab platform.
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quantum star graph analogues of pt symmetric Square Wells part ii spectra
Canadian Journal of Physics, 2015Co-Authors: Miloslav ZnojilAbstract:For the non-Hermitian equilateral q-pointed star-shaped quantum graphs of our previous paper (Can. J. Phys. 90, 1287 (2012) doi:10.1139/p2012-107) we show that because of certain dynamical aspects ...
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quantum star graph analogues of pt symmetric Square Wells ii spectra
arXiv: Quantum Physics, 2014Co-Authors: Miloslav ZnojilAbstract:For non-Hermitian equilateral q-pointed star-shaped quantum graphs of paper I [Can. J. Phys. 90, 1287 (2012), arXiv 1205.5211] we show that due to certain dynamical aspects of the model as controlled by the external, rotation-symmetric complex Robin boundary conditions, the spectrum is obtainable in a closed asymptotic-expansion form, in principle at least. Explicit formulae up to the second order are derived for illustration, and a few comments on their consequences are added.
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a generalized family of discrete mathcal pt symmetric Square Wells
International Journal of Theoretical Physics, 2013Co-Authors: Miloslav ZnojilAbstract:N-site-lattice Hamiltonians H(N) are introduced and perceived as a set of systematic discrete approximants of a certain \(\mathcal {PT}\)-symmetric Square-well-potential model with the real spectrum and with a non-Hermiticity which is localized near the boundaries of the interval. Its strength is controlled by one, two or three parameters. The problem of the explicit construction of a nontrivial metric which makes the theory unitary is then addressed. It is proposed and demonstrated that due to the not too complicated (viz., tridiagonal matrix) form of our input Hamiltonians, the computation of the metric is straightforward and that its matrix elements prove obtainable, non-numerically, in elementary polynomial forms.
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a generalized family of discrete pt symmetric Square Wells
arXiv: Quantum Physics, 2013Co-Authors: Miloslav ZnojilAbstract:N-site-lattice Hamiltonians H are introduced and perceived as a set of systematic discrete approximants of a certain PT-symmetric Square-well-potential model with the real spectrum and with a non-Hermiticity which is localized near the boundaries of the interval. Its strength is controlled by one, two or three parameters. The problem of the explicit construction of a nontrivial metric which makes the theory unitary is then addressed. It is proposed and demonstrated that due to the not too complicated tridiagonal-matrix form of our input Hamiltonians the computation of the metric is straightforward and that its matrix elements prove obtainable, non-numerically, in elementary polynomial forms.
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quantum star graph analogues of pt symmetric Square Wells
Canadian Journal of Physics, 2012Co-Authors: Miloslav ZnojilAbstract:We recall the solvable 𝒫𝒯-symmetric quantum Square well on an interval of x ∈ (–L, L) := G(2) (with an α-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval G(2) (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a q-pointed equilateral star graph G(q) endowed with the simplest complex-rotation-symmetric external α-dependent Robin boundary conditions. The remarkably compact form of the secular determinant is then deduced. Its analysis reveals that (i) at any integer q = 2, 3, …, there exists the same q-independent and infinite subfamily of the real energies, and (ii) at any special q = 2, 6, 10, …, there exists another, additional, q-dependent infinite subfamily of the real energies. In the spirit of the recently proposed dynamical construction of the Hilbert space of a quantum system, the physical bound-state interpretation of these eigenvalues is finally proposed.
Christopher Ticknor - One of the best experts on this subject based on the ideXlab platform.
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model for scattering with proliferating resonances many coupled Square Wells
Physical Review A, 2018Co-Authors: Nirav P Mehta, Kaden R A Hazzard, Christopher TicknorAbstract:We present a multichannel model for elastic interactions, composed of an arbitrary number of coupled finite Square-well potentials, and derive semianalytic solutions for its scattering behavior. Despite the model's simplicity, it is flexible enough to include many coupled short-ranged resonances in the vicinity of the collision threshold, as is necessary to describe ongoing experiments in ultracold molecules and lanthanide atoms. We also introduce a simple but physically realistic statistical ensemble for parameters in this model. We compute the resulting probability distributions of nearest-neighbor resonance spacings and analyze them by fitting to the Brody distribution. We quantify the ability of alternative distribution functions, for resonance spacing and resonance number variance, to describe the crossover regime. The analysis demonstrates that the multichannel Square-well model with the chosen ensemble of parameters naturally captures the crossover from integrable to chaotic scattering as a function of closed-channel coupling strength.
Riccardo Fantoni - One of the best experts on this subject based on the ideXlab platform.
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non existence of a phase transition for the penetrable Square Wells in one dimension
arXiv: Statistical Mechanics, 2010Co-Authors: Riccardo FantoniAbstract:Penetrable Square Wells in one dimension were introduced for the first time in [A. Santos et. al., Phys. Rev. E, 77, 051206 (2008)] as a paradigm for ultra-soft colloids. Using the Kastner, Schreiber, and Schnetz theorem [M. Kastner, Rev. Mod. Phys., 80, 167 (2008)] we give strong evidence for the absence of any phase transition for this model. The argument can be generalized to a large class of model fluids and complements the van Hove's theorem.
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non existence of a phase transition for penetrable Square Wells in one dimension
Journal of Statistical Mechanics: Theory and Experiment, 2010Co-Authors: Riccardo FantoniAbstract:Penetrable Square Wells in one dimension were introduced for the first time in Santos et al (2008 Phys. Rev. E 77 051206) as a paradigm for ultra-soft colloids. Using the Kastner, Schreiber and Schnetz theorem (Kastner 2008 Rev. Mod. Phys. 80 167) we give strong evidence for the absence of any phase transition for this model. The argument can be generalized to a large class of model fluids and complements van Hove's theorem.
R. M. Ricotta - One of the best experts on this subject based on the ideXlab platform.
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Photoinduced Quantum Tunneling Model Applied to an Organic Molecule
Brazilian Journal of Physics, 2020Co-Authors: E. Drigo Filho, K. H. P. Jubilato, R. M. RicottaAbstract:The paper proposes a photoinduced quantum tunneling model of electron transfer through four quantum Square Wells potential to simulate the biological process of photosynthesis in bacteria. The problem is mathematically exact with mathematical transcendental equations solved graphically. This simplified model allowed the calculation of the characteristic tunneling times of the process. A comparison is made between the results obtained in the model and the experimental data of the organic molecule Rhodobacter sphaeroides photosynthetic process.
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photoinduced quantum tunneling through a model of Square Wells potential
arXiv: Quantum Physics, 2019Co-Authors: Elso Drigo Filho, K. H. P. Jubilato, R. M. RicottaAbstract:The paper proposes a photoinduced quantum tunneling model of electron transfer through four quantum Square Wells potential to simulate the biological process of photosynthesis in bacteria. The problem is mathematically exact, given the cyclic process, with mathematical transcendental equations solved graphically. This simplified model allowed the calculation of the characteristic tunneling times of the process. A comparison is made between the results obtained in the model and the experimental data of Rhodobacter sphaeroides photosynthetic process.
Nirav P Mehta - One of the best experts on this subject based on the ideXlab platform.
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model for scattering with proliferating resonances many coupled Square Wells
Physical Review A, 2018Co-Authors: Nirav P Mehta, Kaden R A Hazzard, Christopher TicknorAbstract:We present a multichannel model for elastic interactions, composed of an arbitrary number of coupled finite Square-well potentials, and derive semianalytic solutions for its scattering behavior. Despite the model's simplicity, it is flexible enough to include many coupled short-ranged resonances in the vicinity of the collision threshold, as is necessary to describe ongoing experiments in ultracold molecules and lanthanide atoms. We also introduce a simple but physically realistic statistical ensemble for parameters in this model. We compute the resulting probability distributions of nearest-neighbor resonance spacings and analyze them by fitting to the Brody distribution. We quantify the ability of alternative distribution functions, for resonance spacing and resonance number variance, to describe the crossover regime. The analysis demonstrates that the multichannel Square-well model with the chosen ensemble of parameters naturally captures the crossover from integrable to chaotic scattering as a function of closed-channel coupling strength.