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| Identifier |
000369788 |
| Title |
A driven one dimensional quantum many-body system |
| Alternative Title |
Ένα καθοδηγούμενο μονοδιάστατο κβαντικό σύστημα πολλών σωματιδίων |
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Author
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Μακρή, Ελεάνα
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Thesis advisor
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Zώτος, Ξενοφών
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| Abstract |
The theoretical study of time-dependent phenomena in quantum
many-body systems is a challenging problem and remains to a large
extent unexplored. In this work we examine the time evolution
of a half-filled 1-D lattice of hard-core bosons driven by a static
field through the numerical study of the time-evolution operator
of the system calculated over one Bloch period. The Hamiltonian
of the problem is mapped to the spin-1/2 1-D Heisenberg model
via the Jordan-Wigner transformation. The evolution operator is
calculated as the time-ordered product of operators describing the
system evolution in elementary steps. Then the effect of the system
parameters on the structure of the spectrum of the evolution operator
is examined. We observe a transition of the spectrum from
irregular to regular as the intensity of the driving increases. On
the other hand, we observe a wider distribution of the eigenvalues
as the repulsive interaction between nearest-neighbours increases.
The presence of an impurity breaks the integrability, causing a lift
of the degeneracies in the spectrum. The particle current expectation
value is expressed in terms of the evolution operator eigenvalues
and eigenfunctions and is then related to the spectrum of the
evolution operator for various system parameters. In most cases
the structure of the spectrum is reflected to the behaviour of the
particle current. Finally, a roughly linear increase of the particle
current expectation value is observed for the integrable system
with strong particle interactions at the adiabatic limit.
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| Language |
English |
| Subject |
Hard-core bosons |
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Integrability |
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Time evolution operator |
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Ολοκληρωσιμότητα |
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Τελεστής χρονικής εξέλιξης |
| Issue date |
2011-11-18 |
| Collection
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School/Department--School of Sciences and Engineering--Department of Physics--Post-graduate theses
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Type of Work--Post-graduate theses
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| Views |
530 |
A driven one dimensional quantum many-body system
