3 research outputs found
Quantum Butterfly Effect at the Crossroads of Spontaneous Symmetry Breaking
In classical mechanics, spontaneous symmetry breaking of the Hamiltonian can
embroil the dynamics of some regular systems into chaos. The classical and
quantum pictures are not entirely different in these broken symmetric regions.
There exists a correspondence between them, but for a brief time window.
However, our numerical observations show that quantum mechanics can emulate the
opposite role and forge exponential fluctuations in classically non-chaotic
systems within an early-time window by introducing a symmetry-breaking term to
the Hamiltonian. In this work, we spontaneously break the existing symmetry in
three one-dimensional quantum mechanical models by varying perturbation
strength to bring anomaly into the system. With the help of numerical
diagnostic tools such as OTOC, Loschmidt echo and spectral form factor(SFF) we
detect the anomalies that may sweep into the system with the introduction of
the asymmetry. Our primary focus is on the exponential growth of OTOC as it
reduces to the Lyapunov exponent in the classical limit. However, these
exponential growths of OTOC are not widespread over the entire potential well
but are limited only to the eigenstates in the neighbourhood of the broken
symmetry. These results suggest that the exponential growth of OTOC, backed by
Loschmidt echo and SFF, is due to asymmetry. In other words, OTOC detects the
effect of symmetry-breaking, which is often synonymous with the butterfly
effect.Comment: 16 pages, 51 figure
Dynamics of a Charged Thomas Oscillator in an External Magnetic Field
In this letter, we provide a detailed numerical examination of the dynamics
of a charged Thomas oscillator in an external magnetic field. We do so by
adopting and then modifying the cyclically symmetric Thomas oscillator to study
the dynamics of a charged particle in an external magnetic field. These
dynamical behaviours for weak and strong field strength parameters fall under
two categories; conservative and dissipative. The system shows a complex
quasi-periodic attractor whose topology depends on initial conditions for high
field strengths in the conservative regime. There is a transition from
adiabatic motion to chaos on decreasing the field strength parameter. In the
dissipative regime, the system is chaotic for weak field strength and weak
damping but shows a limit cycle for high field strengths. Such behaviour is due
to an additional negative feedback loop that comes into action at high field
strengths and forces the system dynamics to be stable in periodic oscillations.
For weak damping and weak field strength, the system dynamics mimic Brownian
motion via chaotic walks.Comment: 9 pages, 48 figure