Satrajit Adhikari

Bio: Satrajit Adhikari is an academic researcher from Indian Association for the Cultivation of Science. The author has contributed to research in topics: Diabatic & Hamiltonian (quantum mechanics). The author has an hindex of 26, co-authored 144 publications receiving 2181 citations. Previous affiliations of Satrajit Adhikari include Indian Institutes of Technology & University of Copenhagen.

Extended Born-Oppenheimer equation for a three-state system.

Abstract: We present explicit forms of nonadiabatic coupling (NAC) elements of nuclear Schrodinger equation (SE) for a coupled three-state electronic manifold in terms of mixing angles of real electronic basis functions. If the adiabatic-diabatic transformation (ADT) angles are the mixing angles of electronic bases, ADT matrix transforms away the NAC terms and brings diabatic form of SE. ADT and NAC matrices are shown to satisfy a curl condition with nonzero divergence. We have demonstrated that the formulation of extended Born-Oppenheimer (EBO) equation from any three-state BO system is possible only when there exists a coordinate-independent ratio of the gradients for each pair of mixing angles. On the contrary, since such relations among the mixing angles lead to zero curl, we explore its validity analytically around conical intersection(s) and support numerically considering two nuclear-coordinate-dependent three surface BO models. Numerical calculations are performed by using newly derived diabatic and EBO equations and expected transition probabilities are obtained.

Extended approximated Born-Oppenheimer equation. I. Theory

Abstract: In this study we consider Born-Oppenheimer coupled equations with the aim of deriving a single approximated Born-Oppenheimer-type equation which contains the effect of the nonadiabatic coupling terms. The derivation is done for a situation where N (\ensuremath{\geqslant}2) adiabatic surfaces, including the ground-state surface, have a degeneracy along a single line (e.g., conical intersection). The new equation can be considered as an extended version of the Born-Oppenheimer approximation. Although derived for a nongeneral case, the extension to a general case is also discussed. As special cases we treat, in the present paper, the two-state system and, in the following paper, the three-state system.

The conical intersection effects and adiabatic single-surface approximations on scattering processes: A time-dependent wave packet approach

Abstract: Using a quasi-Jahn-Teller model and an extended version of the approximate Born-Oppenheimer (BO) single surface equations, Baer, Charutz, Kosloff, and Baer [J. Chem. Phys. 105, 9141 (1996)] have performed time-independent scattering calculations to study a direct effect on the symmetry of the nuclear wave function due to conical intersections between BO potential energy surfaces. In this article, we have addressed the same problem using the same model by introducing either a vector potential in the nuclear Hamiltonian or by incorporating a phase factor in the nuclear wave function. The scattering calculations have been carried out by using a time-dependent wave packet approach.

Electronic read-out of a single nuclear spin using a molecular spin transistor

Abstract: The long-lived nuclear spin state of an individual metal atom embedded in a single-molecule magnet is shown to be readable electronically. Nuclear spins are increasingly being considered for the role of active elements in a quantum computer: in contrast to electronic spins they are well isolated from the environment, a favourable condition for achieving stable quantum coherence. The challenge is to address and manipulate these spins. Romain Vincent et al. bring such applications closer by showing that the long-lived nuclear-spin state of an individual metal atom embedded in a single-molecule magnet can be read electronically. They observe long nuclear-spin lifetimes — tens of seconds — and are able to determine the dynamics of spin states. Quantum control of individual spins in condensed-matter devices is an emerging field with a wide range of applications, from nanospintronics1,2 to quantum computing3. The electron, possessing spin and orbital degrees of freedom, is conventionally used as the carrier of quantum information in proposed devices4,5,6,7,8,9. However, electrons couple strongly to the environment, and so have very short relaxation and coherence times. It is therefore extremely difficult to achieve quantum coherence and stable entanglement of electron spins. Alternative concepts propose nuclear spins as the building blocks for quantum computing10, because such spins are extremely well isolated from the environment and less prone to decoherence. However, weak coupling comes at a price: it remains challenging to address and manipulate individual nuclear spins11,12,13,14. Here we show that the nuclear spin of an individual metal atom embedded in a single-molecule magnet can be read out electronically. The observed long lifetimes (tens of seconds) and relaxation characteristics of nuclear spin at the single-atom scale open the way to a completely new world of devices in which quantum logic may be implemented.

O(N) methods in electronic structure calculations.

Abstract: Linear-scaling methods, or methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high-performance computers. The linear-scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas are then discussed. The applications of linear-scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear-scaling methods are discussed.

A Schematic Model of Baryons and Mesons

Abstract: If we assume that the strong interactions of baryons and mesons are correctly described in terms of the broken "eightfold way", we are tempted to look for some fundamental explanation of the situation. A highly promised approach is the purely dynamical "bootstrap" model for all the strongly interacting particles within which one may try to derive isotopic spin and strangeness conservation and broken eightfold symmetry from self-consistency alone. Of course, with only strong interactions, the orientation of the asymmetry in the unitary space cannot be specified; one hopes that in some way the selection of specific components of the F-spin by electromagnetism and the weak interactions determines the choice of isotopic spin and hypercharge directions.