Calculations of time-dependent observables in non-Hermitian quantum mechanics: The problem and a possible solution

The solutions of the time independent Schrodinger equation for non-Hermitian (NH) Hamiltonians have been extensively studied and calculated in many different fields of physics by using L^2 methods that originally have been developed for the calculations of bound states. The existing non-Hermitian formalism breaks down when dealing with wavepackets(WP). An open question is how time dependent expectation values can be calculated when the Hamiltonian is NH ? Using the F-product formalism, which was recently proposed, [J. Phys. Chem., 107, 7181 (2003)] we calculate the time dependent expectation values of different observable quantities for a simple well known study test case model Hamiltonian. We carry out a comparison between these results with those obtained from conventional(i.e., Hermitian) quantum mechanics (QM) calculations. The remarkable agreement between these results emphasizes the fact that in the NH-QM, unlike standard QM, there is no need to split the entire space into two regions; i.e., the interaction region and its surrounding. Our results open a door for a type of WP propagation calculations within the NH-QM formalism that until now were impossible.Comment: 20 pages, 5 Postscript figures. To be Published in Physical Review

Accelerator dynamics of a fractional kicked rotor

It is shown that the Weyl fractional derivative can quantize an open system. A fractional kicked rotor is studied in the framework of the fractional Schrodinger equation. The system is described by the non-Hermitian Hamiltonian by virtue of the Weyl fractional derivative. Violation of space symmetry leads to acceleration of the orbital momentum. Quantum localization saturates this acceleration, such that the average value of the orbital momentum can be a direct current and the system behaves like a ratchet. The classical counterpart is a nonlinear kicked rotor with absorbing boundary conditions.Comment: Submitted for publication in Phys. Rev.

S-Matrix Poles Close to Thresholds in Confined Geometries

We have studied the behavior of the S-matrix poles near threshold for quantum waveguides coupled to a cavity with a defect. We emphasize the occurrence of both dominant and shadow poles on the various sheets of the energy Riemann surface, and show that the changes of the total conductivity near threshold as the cavity's width changes can be explained in terms of dominant to shadow pole transitions.Comment: 10 pages, 5 figure

The absolute position of a resonance peak

It is common practice in scattering theory to correlate between the position of a resonance peak in the cross section and the real part of a complex energy of a pole of the scattering amplitude. In this work we show that the resonance peak position appears at the absolute value of the pole's complex energy rather than its real part. We further demonstrate that a local theory of resonances can still be used even in cases previously thought impossible

Use of computers to exclude the influence of radiometer instability upon measurement results

A radiometer, practically insensitive to great fluctuations in the equipment amplification coefficient, was developed by dividing the useful signal by a reference signal and modulating the two signals at different frequencies. The signals are simultaneously separated by corresponding synchronous detectors and recorded over two channels. The operation is simplified by replacing the continuous signals by a sampling of discrete values, and using a digital computer. The four steps involved in the process are described and a block diagram is included. This technique not only directly connects the radiometer with the computer, but also records all data provided by the control and signal channels

Epidemiology, Diagnosis and Treatment Outcomes of Skin Melanoma in the Republic of Belarus

The primary incidence of skin melanoma in the Republic of Belarus over 25 years (from 1991 through 2015) has increased 3.3-fold (from 2.6 to 9.0 per 100,000 population). A higher level of urban population incidence, a large proportion of people affected at the employable age. In 2015 the proportion of prognostically unfavourable pT3-pT4 neoplasms was 38.2%. Metastatic disease was detected in 12.4% of the patients. Methodology: Material of the paper is based on the data of Belarusian Cancer Registry using the principles of data collection, monitoring and processing recommended by the IARC. Results: The proportion of stage IB neoplasms made up almost one third of the cases assigned to stage I. Of the cases assigned to stage II, the proportion of neoplasms with a high prognostic index of metastatic spread (T3b-T4b) was more than 70%. The recurrence rate is 15.1% even at melanoma invasion depth of up to 1 mm (with ulceration), while it rises to 32.4% at pT2b. The cumulative 5-year disease-specific survival of all patients in 2005 was 54.1 ± 1.5%, and in 2015 it was 64.0±2.2%. Conclusion: A strong correlation is observed between survival of patients and the extent of invasion and ulceration of the primary focus. For metastasis-free pT1a melanoma, the 5-year survival was 92.2%, for T1b – 79.9%, for pT2b – 72.5%, for pT3b – 55.1%, for pT4b – 49.1%. According to the Cancer Registry data, ulceration of the primary neoplasm is frequently observed: it amounts to 41.1% of the cases with melanoma invasion depth up to 2 mm (pT2), to 55.9% with 2-4 mm (pT3) and to 76.3% with the tumor thickness of more than 4 mm (pT4)

Influence of branch points in the complex plane on the transmission through double quantum dots

We consider single-channel transmission through a double quantum dot system consisting of two single dots that are connected by a wire and coupled each to one lead. The system is described in the framework of the S-matrix theory by using the effective Hamiltonian of the open quantum system. It consists of the Hamiltonian of the closed system (without attached leads) and a term that accounts for the coupling of the states via the continuum of propagating modes in the leads. This model allows to study the physical meaning of branch points in the complex plane. They are points of coalesced eigenvalues and separate the two scenarios with avoided level crossings and without any crossings in the complex plane. They influence strongly the features of transmission through double quantum dots.Comment: 30 pages, 14 figure

Human palaeodiet at Zamostje 2, central Russia:Results of radiocarbon and stable isotope analyses

Only 21 human remains have been identified at Zamostje 2, despite extraordinarily good conditions for organic preservation, and the recovery of thousands of animal bones from layers dating from the Late Mesolithic to the Middle Neolithic (c.6500–4000 cal BC). Almost all the human remains are fragments of the cranium, maxilla, mandible, which are potentially reworked from earlier depositions, uphill or upstream of Zamostje 2, or isolated teeth. Disregarding naturally shed deciduous teeth, these remains have been attributed to between 5 and 14 individuals, ranging in age from 6 to 7 years to mature adult. We report AMS radiocarbon (14C) dating and dietary stable isotopes, δ13C and δ15N, for all the human bones, and δ13C and δ15N values from 63 prehistoric animal bones from Zamostje 2, including 18 fish and 7 dogs. Using the faunal isotope data, we construct isotope signatures for different food groups, which we use to interpret the human δ13C and δ15N values. Based on 14C ages and dietary stable isotopes, we propose that the human bones represent 10–12 individuals, most of whom date to the Late Mesolithic occupation at Zamostje 2; one is somewhat earlier in the Mesolithic, one (probably from the nearby site, Zamostje 1) may date to the Middle Neolithic, and two (one from Zamostje 1, one unprovenanced) date to the Late Neolithic or Eneolithic. The earliest and latest individuals may have obtained most of their dietary protein intake from fish, but Late Mesolithic individuals probably had more mixed diets. Palaeodiet reconstruction is complicated by unusual δ13C and δ15N values for local fish in the Late Mesolithic, which are reflected in δ13C and δ15N values from dogs

Calculation of the Density of States Using Discrete Variable Representation and Toeplitz Matrices

A direct and exact method for calculating the density of states for systems with localized potentials is presented. The method is based on explicit inversion of the operator $E-H$. The operator is written in the discrete variable representation of the Hamiltonian, and the Toeplitz property of the asymptotic part of the obtained {\it infinite} matrix is used. Thus, the problem is reduced to the inversion of a {\it finite} matrix