Dynamical phase transitions in quantum mechanics

2013

Phys. Rev. E

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The states of an open quantum system are coupled via the environment of scattering wave functions. The complex coupling coefficients ω between system and environment arise from the principal value integral and the residuum. At high-level density where the resonance states overlap, the dynamics of the system is determined by exceptional points. At these points, the eigenvalues of two states are equal and the corresponding eigenfunctions are linearly dependent. It is shown in the present paper that Im(ω) and Re(ω) influence the system properties differently in the surrounding of exceptional points. Controlling the system by a parameter, the eigenvalues avoid crossing in energy near an exceptional point under the influence of Re(ω) in a similar manner as it is well known from discrete states. Im(ω), however, leads to width bifurcation and finally (when the system is coupled to one channel, i.e., to one common continuum of scattering wave functions), to a splitting of the system into two parts with different characteristic time scales. The role of observer states is discussed. Physically, the system is stabilized by this splitting since the lifetimes of some states are longer than before, while that of one state is shorter. In the cross section the short-lived state appears as a background term in high-resolution experiments. The wave functions of the long-lived states are mixed in those of the original ones in a comparably large parameter range. Numerical results for the eigenvalues and eigenfunctions are shown for N=2,4, and 10 states coupled mostly to one channel.

Section: Discussionmentioning

confidence: 60%

Width bifurcation and dynamical phase transitions in open quantum systems

Eleuch

2013

Phys. Rev. E

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“…In nuclei ǫ ′ c → ∞ while ǫ c denotes the lowest threshold for emission of a particle. The energy shift ∆ k = E k −E B k , including the corresponding corrections arising from the coupling of different states via the continuum, can not be simulated by two-body forces [10]. It is a global property, see [11], and is not contained in any standard calculation with a Hermitian Hamilton operator for the many-body problem.…”

Section: Non-hermitian Hamilton Operator Of An Open Quantum Systemmentioning

confidence: 99%

“…by the embedding of the system into the continuum of scattering wavefunctions. By this, many-body forces are induced in the system [10]. Discrete states avoid crossing and, at a critical value of the control parameter, the two states are exchanged as known for about 80 years [17].…”

Section: Discrete and Narrow Resonance Statesmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical stabilization and time in open quantum systems

Fortschritte der Physik

2012

The meaning of time in an open quantum system is considered under the assumption that both, system and environment, are quantum mechanical objects. The Hamilton operator of the system is non-Hermitian. Its imaginary part is the time operator. As a rule, time and energy vary continuously when controlled by a parameter. At high level density, where many states avoid crossing, a dynamical phase transition takes place in the system under the influence of the environment. It causes a dynamical stabilization of the system what can be seen in many different experimental data. Due to this effect, time is bounded from below: the decay widths (inverse proportional to the lifetimes of the states) do not increase limitless. The dynamical stabilization is an irreversible process. * rotter@pks.mpg.de

“…6 of [33] and in Sect. 5 of [48], see also [9,10,45,50,51]), some properties of Dicke's superradiance are referred to singular points first in the present paper. The results should be proven by further experimental studies.…”

Section: Discussionmentioning

confidence: 89%

Open quantum systems and Dicke superradiance

Eleuch

2014

Eur. Phys. J. D

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We study generic features of open quantum systems embedded into a continuum of scattering wavefunctions and compare them with results discussed in optics. A dynamical phase transition may appear at high level density in a many-level system and also in a two-level system if the coupling W to the environment is complex and sufficiently large. Here nonlinearities occur. When W ij is imaginary, two singular (exceptional) points may exist. In the parameter range between these two points, width bifurcation occurs as function of a certain external parameter. A unitary representation of the S-matrix allows to calculate the cross section for a two-level system, including at the exceptional point (double pole of the S-matrix). The results obtained for the transition of level repulsion at small (real) W ij to width bifurcation at large (imaginary) W ij show qualitatively the same features that are observed experimentally in the transition from Autler-Townes splitting to electromagnetically induced transparency in optics. Fermi's golden rule holds only below the dynamical phase transition while it passes into an anti-golden rule beyond this transition. The results are generic and can be applied to the response of a complex open quantum system to the action of an external field (environment). They may be considered as a guideline for engineering and manipulating quantum systems in such a way that they can be used for applications with special requirements. * email: hichemeleuch@yahoo.fr † email: rotter@pks.mpg.de Recently, dynamical phase transitions (DPTs) are considered in different open quantum systems. They appear mostly at high level density and are observed experimentally as well as theoretically by using different approaches. Common to all of them is a very robust spectroscopic redistribution that takes place in the system in a critical region of a certain control parameter. As a result of the spectroscopic redistribution, short-lived states appear together with long-lived ones (called usually line width bifurcation) which all have lost their spectroscopic relation to the original states in the subcritical parameter region. Mathematically, the spectroscopic redistribution can be traced back to the existence of singular points in the continuum (called usually exceptional points (EPs)). For details see Appendix A. The DPTs observed in many-body open quantum systems show features which are similar to the Dicke superradiance known in optics [1]. This has been shown some years ago [2] : the DPT observed in a many-body open quantum system [3] is analogue to the formation of the superradiant Dicke state in optics. The simple model used in this study is based on statistical assumptions and can, of course, not explain the sensitive dependence of the system properties on the variation of external parameters. It shows however the meaning of the imaginary part of the coupling term between system and environment for the formation of the so-called superradiant (short-lived) and subradiant (long-lived) states in a many-body open quan...