The bogoliubovdegennes hamiltonian is a meanfield hamiltonian, that is, a onebody quadratic hamiltonian. A variational approach to bogoliubov excitations and. We study the ground state properties of the system by evolving in imaginary time the eulerlagrange equation derived from the variational principle. To go beyond the linear regime of the bogoliubov stability analysis, we simulate. Comparing the full timedependent bogoliubovdegennes. Use features like bookmarks, note taking and highlighting while reading bogoliubovde gennes method and its applications lecture notes in physics book 924. A systematic discussion is given of the approximate free energies of complex statistical systems. The code is suitable for handling quantum fluctuations as well as thermal fluctuations at temperatures. A general method for the construction of tbcs for multicomponent schrodinger k. In theoretical physics, the bogoliubov transformation, also known as bogoliubov valatin transformation, were independently developed in 1958 by nikolay bogolyubov and john george valatin for finding solutions of bcs theory in a homogeneous system. Conventional superconductors 1 bogoliubovde gennes equation.
The book will be useful for gradient students and all those interested in moderate problems of superconductivity. Bosonic linear unitary bogoliubov transformation reduction. Linear and nonlinear bullets of the bogoliubovde gennes. Evolution as a canonical transformation remarkably, the evolution of a dynamical system can be considered as a canonical transformation. This induces an autoequivalence on the respective representations. We develop a fortran code to compute fluctuations in atomic condensates. Conventional superconductors 1 bogoliubovde gennes equation for inhomogeneous superconductivity. Computational condensed matter northeastern university.
Bogoliubov hamiltonian and elementary excitations unitrento. This program, for herons formula, reads data on a tape reel containing three 5digit integers a, b, and c as. Transparent boundary conditions for the bogoliubovde gennes. We find that the calculated excitation spectrum shows indeed a roton minimum, and the. Beyond mean field effects in quasi1d dipolar bosonic. The lecture notes discuss the bogoliubovdegennes bdg method and its applications in superconductivity. Exploiting the modification of the dispersion relation induced by the modulation, we demonstrate the existence of localized structures of the. The bdg equations are recast as matrix equations and solved self consistently. The bogoliubovde gennes equations are used for a number of theoretical works on the trapped boseeinstein condensates.
A collection of fortran codes for large scale scientific. Electronhole coherent states for the bogoliubovde gennes. The cyclic tridiagonal matrix associated with the harper equation is then tridiagonalized by another unitary transformation. Bogoliubovde gennes equations lisc software homepage. We report on the focalization of bogoliubovde gennes excitations of the nonlinear schrodinger equation in the defocusing regime grosspitaevskii equation for repulsive boseeinstein condensates with a spatially modulated periodic potential. Fortran toolbox for calculating fluctuations in atomic.
We develop a fortran code to compute fluctuations in atomic condensates fact by solving the bogoliubovde gennes bdg equations for two component. This release integrates an updated compiler, minor cosmetic improvements, and bug fixes within the integrated development environment. For initial states that are close to thermal equilibrium states at temperatures near the critical temperature, we show that the magnitude of the order parameter stays approximately constant in time and, in particular, does not follow a timedependent ginzburg. The purpose of this book is to provide an elementary yet systematic description of the bogoliubovde gennes bdg equations, their unique symmetry properties. Gravitationally bound bcs state as dark matter journal. Leggett lecture 11 the bogoliubovde gennes and andreev equations. We show that, even above the critical temperature, the full equations and their linear approximation give rise to completely different. Conventional superconductors 1 bogoliubovde gennes. The program uses realistic potentials in the spinsingle and spintriplet configurations, and is able to calculate densitydependent.
A simple and useful plotting program, gnuplot, is freely available in the web, and. The aim is not that of give a complete and exhaustive treatment of canonical transformations. Of course this didnt help us to achieve our aim, so lets pair the majoranas differently. The bogoliubov transformation is also important for understanding the unruh effect, hawking radiation, pairing effects in nuclear physics, and many other topics. Topological insulators dirac equation in condensed matters shunqing shen. Sep 05, 2016 the open fortran project ofp provides a fortran 2008 compliant parser and associated tools. Abstract we develop a fortran code to compute fluctuations in atomic condensates fact by solving the bogoliubovde gennes bdg equations for two component boseeinstein condensate tbec in. These tools provide a java and c api for actions called when parser rules are completed.
This operator is defined by the corresponding transformation up to an arbitrary phase factor. Bdg solver for bogoliubovde gennes equations for type ii superconductors in external magnetic field approximately 5,000 lines of fortran 90 code. The bogoliubov transformation is an isomorphism of either the canonical commutation relation algebra or canonical anticommutation relation algebra. We develop a fortran code to compute fluctuations in atomic condensates fact by solving the bogoliubovde gennes bdg equations for two component boseeinstein condensate tbec in quasitwo dimensions. The windows and macos packages for simply fortran now include the gnu fortran compiler version 9. The heisenberg equation is equivalent to the dynamical version of the bogoliubovde gennes equation. Chapter 2 theoretical concepts universiteit leiden. Topological insulators dirac equation in condensed matters. The code is suitable for handling quantum fluctuations as well as thermal fluctuations at. View ian robert georges profile on angellist, the startup and tech network software engineer austin physics degree, ut austin, focus on condensed matter theory, turned data engineer. Variational principle of bogoliubov and generalized mean.
Fortran programs for the timedependent grosspitaevskii equation in a fully. A method of studying the bogoliubovde gennes equations. From the hamiltonian and the commutation rules one can identify and as the creation and annihilation operators of quasiparticles with energy. If all the engenvalues are real, the corresponding free hamiltonian is diagonalized in the bosonic.
These excitations fill the core, making direct imaging of the vortex unlikely. Introduction in this lecture notes, we discuss canonical transformations in the context of quantum field theory qft. But avoid asking for help, clarification, or responding to other answers. We are also exploring magnetic effects as well as long junction effects using the phenomenological sinegordon equation.
Thanks for contributing an answer to computational science stack exchange. Device modeling consists of both microscopic and mesoscopic methods for proper simulation of device operation. Some limitations of the static gp differential equation are thereby removed, though it is a matter of further study to determine whether a correlated wave function exists as underpinning for the. The bogoliubovde gennes equations are solved di rectly and numerically. These equations are known to give the energies of the quasiparticles when all the eigenvalues are real. The purpose of this book is to provide an elementary yet systematic description of the bogoliubovde gennes bdg equations, their unique symmetry properties and their relation to greens function the. Thanks for contributing an answer to mathematica stack exchange. Programs are parallelized utilizing message passing.
In theoretical physics, the bogoliubov transformation, also known as bogoliubovvalatin transformation, were independently developed in 1958 by nikolay bogolyubov and john george valatin for finding solutions of bcs theory in a homogeneous system. Transparent boundary conditions for the swave bogoliubovde gennes equations. Electronhole coherent states for the bogoliubovde gennes equation sven gnutzmann, 1. We show that, even above the critical temperature, the full equations and their linear approximation give rise to completely. Fortran 90 and the gramschmidt orthonormalization, we obtain an. We develop a fortran code to compute fluctuations in atomic condensates fact by solving the bogoliubovde gennes bdg equations for. Transparent boundary conditions for the bogoliubovde. It also provides fortran interfaces to the opencl runtime new. Numerical construction of a lowenergy effective hamiltonian in a. The obtained truncated eigenbasis is utilized to expand the bogoliubov. Bogoliubovde gennes method and its applications lecture notes in physics series by jianxin zhu. We could have, instead, assumed the expectation was nonzero for pairs with a nonzero total momentum.
Accordingly, the bcslike reduction procedureis required to choose a correct. Nuclear dynamics of triatomic molecules on excited potential energy surfaces bdgtmat. Bogoliubovde gennes method and its applications lecture notes in physics book 924 kindle edition by zhu, jianxin. We develop a fortran code to compute fluctuations in atomic condensates fact by solving the bogoliubovde gennes bdg equations. In section 2 we propose a choice of this phase factor so that the bogoliubov. Pairingin thebogoliubovdegennes equations yongjihn kim department ofphysics,purdueuniversity,westlafayette, indiana47907 abstract it is shown that the bogoliubovde gennes equations pair the electrons in states which are linear combinations of the normal states.
Download it once and read it on your kindle device, pc, phones or tablets. Bosonic linear unitary bogoliubov transformation reduction theorem samuel l. Please read our short guide how to send a book to kindle. Solution of the bogoliubovde gennes equations using multichannel scattering methods bdgtmat. Bogoliubov theory for bose gases in random potentials. Approximatrix is happy to announce the release of simply fortran version 3. In this work we provide software that was developed for the specific purpose to. We want only one majorana to remain at an edge, so lets pair up the majoranas from adjacent sites, leaving the first one and. Incompatibility of timedependent bogoliubovdegennes and. We therefore largely follow this approach and notation in the main body of this work. The code is suitable for handling quantum fluctuations as. Bogoliubovde gennes method and its applications jianxin zhu.
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