Time Asymmetric Quantum Mechanics and Shock Waves: Exploring the Irreversibility in Nonlinear Optics

Abstract

The description of irreversible phenomena is a still debated topic in quantum mechanics. Still nowadays, there is no clear procedure to distinguish the coupling with external baths from the intrinsic irreversibility in isolated systems. In 1928 Gamow introduced states with exponentially decaying observables not belonging to the conventional Hilbert space. These states are named Gamow vectors, and they belong to rigged Hilbert spaces. This review summarizes the contemporary approach using Gamow vectors and rigged Hilbert space formalism as foundations of a generalized "time asymmetric" quantum mechanics. We study the irreversible propagation of specific wave packets and show that the topic is surprisingly related to the problem of irreversibility of shock waves in classical nonlinear evolution. We specifically consider the applications in the field of nonlinear optics. We show that it is possible to emulate irreversible quantum mechanical process by the nonlinear evolution of a laser beam and we provide experimental tests by the generation of dispersive shock waves in highly nonlocal regimes. We demonstrate experimentally the quantization of decay rates predicted by the time-asymmetric quantum mechanics. This work furnishes support to the idea of intrinsically irreversible wave propagation, and to novel tests of the foundations of quantum mechanics.

Optical spatial shock waves in nonlocal nonlinear media

“…2 the derivation of nonlocal NLSE was detailed, and main features of wave breaking in thermal Kerr media were reported [27]. In order to exhibit the theoretical interpretations of these phenomena as intrinsically irreversible, TAQM and turbulence wave theory approaches were summarized [11,37,39]. Section 3 is a collection of experiments on DSW generation in thermal media, first about a quite rich literature on observations in Rhodamine [27], and their TAQM explaination [35,36,38].…”

“…Dispersive shock waves (DSWs) are rapidly oscillating solutions of hyperbolic partial differential equations that contrast the generation of multivalued regions through the formation of undular bores [1][2][3][4][5][6][7][8][9][10][11]. This class of phenomena was investigated in several physical fields, initially in shallow water waves [12] and ion-acoustic waves [13], then in oceanography [14], pulses propagation in photonic fibers [15,16], Bose-Einstein condensates [17][18][19][20][21][22], quantum liquids [23], photorefractive media [24], plasma physics [25], viscous fluids [26], and diffracting optical beams [5,[27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

“…For many years, Whitham modulation and hydrodynamic approximation have predominated in solving the nonlocal NLSE [2,27]. However, hydrodynamic approximation cannot describe light propagating beyond the shock point, and two new techniques have been developed, one coming from nuclear physics, the time asymmetric quantum mechanics (TAQM) [11,[56][57][58][59][60][61][62][63][64][65][66], which models the nonlinear wave intrinsically irreversible propagation as a superposition of decaying resonances, and the wave turbulence theory [31,37,39,[67][68][69], which uses a statistical interpretation of nonlinear optics.…”

Incoherent Shock and Collapse Singularities in Non-Instantaneous Nonlinear Media

“…[14,15,85] in the spatial domain (non-local non-linearity), the evolution of the coherent field can be described by effective equations that are analogous to the hydrodynamic model (3) and (4), which precisely predicts the CSCS. Interestingly, the development of the shock singularity has been recently discussed in analogy with the quantum squeezing effect in phase-space [86], while its actual irreversible behavior has been discussed in relation to Gamow vectors [87]. Note in Figure 7 that, by starting from a coherent pulse, the post-collapse dynamics evidence the formation of an erratic dynamics of the field, as illustrated by NLS simulations in Figure 7.…”

Anisotropic Optical Shock Waves in M-Cresol/Nylon Highly Nonlocal Nonlinearity

“…(8) |φ(z) = e −ıĤRHOz |ψ even x e −ıĤRHOz |ψ even y . The representation of |φ even (z) x,y = e −ıĤRHOz |ψ even x,y in terms of GVs was already studied and was also already demonstrated to describe 1D DSWs in thermal media [25,26,28,35,56]. It is |φ even (z)…”