Essays about: "Hamiltonian mechanics"

Showing result 6 - 10 of 21 essays containing the words Hamiltonian mechanics.

  1. 6. Dynamics at an exceptional point in an interacting quantum dot system

    University essay from Lunds universitet/Fasta tillståndets fysik; Lunds universitet/Fysiska institutionen

    Author : William Samuelson; [2022]
    Keywords : Physics and Astronomy;

    Abstract : A fundamental postulate of quantum mechanics is that the Hamiltonian of a closed system is Hermitian, guaranteeing real-valued energies and conserved probabilities throughout the evolution of the system. However, for quantum systems where there is dissipation and crosstalk with the environment, such as a system of quantum dots connected to an environment of metallic leads, the dynamics of the system is instead generated by a non-Hermitian Liouvillian superoperator. READ MORE

  3. 7. Theories with higher-order time derivatives and the Ostrogradsky ghost

    University essay from Stockholms universitet/Fysikum

    Author : Eleonora Svanberg; [2022]
    Keywords : Ostrogradsky ghost; higher-order time derivatives theories; Lagrangian mechanics; mathematical physics; Hamiltonian formalism;

    Abstract : Newton's second law, Schrödinger's equation and Maxwell's equations are all theories composed of at most second-time derivatives. Indeed, it is not often we need to take the time derivative of the acceleration. READ MORE

  4. 8. On a novel soliton equation, its integrability properties, and its physical interpretation

    University essay from KTH/Fysik

    Author : Alexander Fagerlund; [2022]
    Keywords : Calogero-Moser systems; Conservation laws; Elliptic dynamics; Fluid dynamics; Hamiltonian mechanics; Hyperbolic dynamics; Integrability; Lax pairs; Pole ansatz; Riemann-Hilbert problems; Solitons; Bevarandelagar; Calogero-Mosersystem; Elliptisk dynamik; Fluiddynamik; Hamiltonmekanik; Hyperbolisk dynamik; Integrabilitet; Laxpar; Polansats; Riemann-Hilbertproblem; Solitoner;

    Abstract : In the present work, we introduce a never before studied soliton equation called the intermediate mixed Manakov (IMM) equation. Through a pole ansatz, we prove that the equation has N-soliton solutions with pole parameters governed by the hyperbolic Calogero-Moser system. READ MORE

  5. 9. Topological Band Theory, An Overview

    University essay from Göteborgs universitet / Institutionen för fysik

    Author : Jens Roderus; [2021-06-14]
    Keywords : ;

    Abstract : Topological insulators, superconductors and semi-metals are states of ma er with unique features such as quantized macroscopic observables and robust, gapless edge states. ese states can not be explained by standard quantum mechanics, but require also the framework of topology to be properly characterized. READ MORE

  6. 10. A Mathematical Analysis of the Harmonic Oscillator in Quantum Mechanics

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Philip Solarz; [2021]
    Keywords : Functional Analysis; Quantum Mechanics; Harmonic Oscillator; Schrödinger Equation; Hamiltonian Operator; Hermite Functions; Hilbert Space; Schatten-von Neumann Operator; Mehler s Formula;

    Abstract : In this paper we derive the eigenfunctions to the Hamiltonian operator associated with the Harmonic Oscillator, and show that they are given by the Hermite functions. Then we prove that the Hermite functions form an orthonormal basis in the underlying Hilbert space. READ MORE