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Study of Quantum Quench in Some Simple Quantum Mechanical Systems

Jafarizadeh, Arash | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50451 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rouhani, Shahin
  7. Abstract:
  8. Classical quench is the act of sudden change in the temperature of a system. This process is not new and has been used in some branches of science, like the smithing industry to produce a hard and stiff metal objects. Quantum Quench is the deformation of system's Hamiltonian in short time interval. This quantum version of quench is around for a few years and has attracted a lot of attention after its experimental realization in Ultracold Atoms setup. Suppose we have hamiltonian which depends on the constant g_0 which is the dynamical parameter of the system. It could be interaction strength between elements in the system or the external electric field amplitude on the system. At an arbitrary time, we change g_0 to the new value, g' abruptly. It is called Quantum Quench which drives the system out of equilibrium. This kind of quench could have different types. If an isolated system is quenched, its energy will change, this will lead to creation of excitations. In this dissertation, we will study the response of the system to this sudden change and will quench two systems. First, a simple harmonic oscillator and second, a scale-invariant quantum mechanics which both are integrable. With calculation of correlation function analytically, the response of systems can be analyzed. Our results show that the excess energy, due to the quench, doesn't spread out between system's degrees of freedom. Therefore these systems will not reach a steady state after the quench which also means that the system would keep a memory of its initial condition. Another noticeable observation after the quench is the symmetry breaking of the system. In simple harmonic oscillator the time-translational symmetry breaks down as the result of quantum quench, and in scale invariant quantum system this scale symmetry breaks down consequently
  9. Keywords:
  10. Conformal Invariance ; Scale Invariance ; Quantum Mechanics ; Quench ; Quantum Quench

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