ترغب بنشر مسار تعليمي؟ اضغط هنا

Fall-to-the-centre as a $mathcal{PT}$ symmetry breaking transition

256   0   0.0 ( 0 )
 نشر من قبل Duncan O'Dell
 تاريخ النشر 2021
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

The attractive inverse square potential arises in a number of physical problems such as a dipole interacting with a charged wire, the Efimov effect, the Calgero-Sutherland model, near-horizon black hole physics and the optics of Maxwell fisheye lenses. Proper formulation of the inverse-square problem requires specification of a boundary condition (regulator) at the origin representing short-range physics not included in the inverse square potential and this generically breaks the Hamiltonians continuous scale invariance in an elementary example of a quantum anomaly. The systems spectrum qualitatively changes at a critical value of the inverse-square coupling, and we here point out that the transition at this critical potential strength can be regarded as an example of a $mathcal{PT}$ symmetry breaking transition. In particular, we use point particle effective field theory (PPEFT), as developed by Burgess et al [J. High Energy Phys., 2017(4):106, 2017], to characterize the renormalization group (RG) evolution of the boundary coupling under rescalings. While many studies choose boundary conditions to ensure the system is unitary, these RG methods allow us to systematically handle the richer case of nonunitary physics describing a source or sink at the origin (such as is appropriate for the charged wire or black hole applications). From this point of view the RG flow changes character at the critical inverse-square coupling, transitioning from a sub-critical regime with evolution between two real, unitary fixed points ($mathcal{PT}$ symmetric phase) to a super-critical regime with imaginary, dissipative fixed points ($mathcal{PT}$ symmetry broken phase) that represent perfect-sink and perfect-source boundary conditions, around which the flow executes limit-cycle evolution.



قيم البحث

اقرأ أيضاً

Bose-Einstein condensates with balanced gain and loss in a double-well potential have been shown to exhibit PT-symmetric states. As proposed by Kreibich et al [Phys. Rev. A 87, 051601(R) (2013)], in the mean-field limit the dynamical behaviour of thi s system, especially that of the PT-symmetric states, can be simulated by embedding it into a Hermitian four-well system with time-dependent parameters. In this paper we go beyond the mean-field approximation and investigate many-body effects in this system, which are in lowest order described by the single-particle density matrix. The conditions for PT symmetry in the single-particle density matrix cannot be completely fulfilled by using pure initial states. Here we show that it is mathematically possible to achieve exact PT symmetry in the four-well many-body system in the sense of the dynamical behaviour of the single-particle density matrix. In contrast to previous work, for this purpose, we use mixed initial states fulfilling certain constraints and use them to calculate the dynamics.
Non-Hermitian systems with parity-time reversal ($mathcal{PT}$) or anti-$mathcal{PT}$ symmetry have attracted a wide range of interest owing to their unique characteristics and counterintuitive phenomena. One of the most extraordinary features is the presence of an exception point (EP), across which a phase transition with spontaneously broken $mathcal{PT}$ symmetry takes place. We implement a Floquet Hamiltonian of a single qubit with anti-$mathcal{PT}$ symmetry by periodically driving a dissipative quantum system of a single trapped ion. With stroboscopic emission and quantum state tomography, we obtain the time evolution of density matrix for an arbitrary initial state, and directly demonstrate information retrieval, eigenstates coalescence, and topological energy spectra as unique features of non-Hermitian systems.
59 - Shiguang Rong , Qiongtao Xie , 2018
Dynamics of a simple system, such as a two-state (dimer) model, are dramatically changed in the presence of interactions and external driving, and the resultant unitary dynamics show both regular and chaotic regions. We investigate the non-unitary dy namics of such a dimer in the presence of balanced gain and loss for the two states, i.e. a $mathcal{PT}$ symmetric dimer. We find that at low and high driving frequencies, the $mathcal{PT}$-symmetric dimer motion continues to be regular, and the system is in the $mathcal{PT}$-symmetric state. On that other hand, for intermediate driving frequency, the system shows chaotic motion, and is usually in the $mathcal{PT}$-symmetry broken state. Our results elucidate the interplay between the $mathcal{PT}$-symmetry breaking transitions and regular-chaotic transitions in an experimentally accessible toy model.
We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact diagonalization, and the Keldysh formalism, we analyze the critica l phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. The physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, $Z_{2}$ symmetry breaking, $mathcal{PT}$ symmetry, state squeezing, and critical fluctuations. Due to its simplicity and solvability, this model can serve as a paradigm for exploration of open quantum many-body physics.
Parity-time ($mathcal{PT}$) symmetric systems are classical, gain-loss systems whose dynamics are governed by non-Hermitian Hamiltonians with exceptional-point (EP) degeneracies. The eigenvalues of a $mathcal{PT}$-symmetric Hamiltonian change from re al to complex conjugates at a critical value of gain-loss strength that is called the $mathcal{PT}$ breaking threshold. Here, we obtain the $mathcal{PT}$-threshold for a one-dimensional, finite Kitaev chain -- a prototype for a p-wave superconductor -- in the presence of a single pair of gain and loss potentials as a function of the superconducting order parameter, on-site potential, and the distance between the gain and loss sites. In addition to a robust, non-local threshold, we find a rich phase diagram for the threshold that can be qualitatively understood in terms of the band-structure of the Hermitian Kitaev mo del. In particular, for an even chain with zero on-site potential, we find a re-entrant $mathcal{PT}$-symmetric phase bounded by second-order EP contours. Our numerical results are supplemented by analytical calculations for small system sizes.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا