Time nonspecial quantum mechanics.

Edward James Anderson

Roland L. Omnes

Wencong Wang, Y. T. Liang, Sicong Xi +3 more

On-chip non-Hermitian dynamic systems based on dissipative engineering have achieved remarkable results, but intrinsic losses and Langevin noise limit the further development of on-chip non-Hermitian devices. In this article, we propose a simple and feasible on-chip gain-gain coupling fully quantum non-Hermitian sensing model based on quasi-phase-matched second-order degenerate parametric downconversion in periodically poled LiNbO 3 waveguides and demonstrate the feasibility of the theory through finite element simulations. Our theory suggests that this model exhibits hidden quadrature pseudo-PT (parity-time) symmetry behavior and gives rise to the phenomenon of competitive amplification between downconverted photons. Additionally, based on quantum Fisher information, our proposed scheme can achieve quantum-sensing enhancement in the full PT-symmetric domain and super-Heisenberg scaling close to the exceptional point (EP). For detuning disturbances, our system exhibits excellent robustness in the nonspecial EP region. These findings will introduce a new perspective for the development of on-chip non-Hermitian technologies and promote the development of non-Hermitian quantum-sensing theories.

C. K. Raju

Ivan Balog, Lucija Nora Farkaš, Maroje Marohnić +1 more

We explore the application of the nonperturbative functional renormalization group (NPFRG), within its most common approximation scheme based on truncations of the derivative expansion, to the Z_{2}-symmetric scalar φ^{4} theory as the lower critical dimension d_{lc} is approached. We aim to assess whether the NPFRG-a broad, nonspecialized method which is accurate in d≥2-can capture the effect of the localized (droplet) excitations that drive the disappearance of the phase transition in d_{lc} and control the critical behavior as d→d_{lc}. We extend a prior analysis to the next (second) order of the derivative expansion to check the convergence of the results and the robustness of the conclusions. The study turns out to be much more involved. Through extensive numerical and analytical work we provide evidence that the convergence to d_{lc} is nonuniform in the field dependence and is characterized by the emergence of a boundary layer near the minima of the fixed-point effective potential. This is the mathematical mechanism through which the NPFRG within the truncated derivative expansion reproduces nontrivial features predicted by the droplet theory of Bruce and Wallace [Phys. Rev. Lett. 47, 1743 (1981)0031-900710.1103/PhysRevLett.47.1743; J. Phys. A: Math. Gen. 16, 1721 (1983)0305-447010.1088/0305-4470/16/8/018], namely, the existence of two distinct small parameters as d→d_{lc} that control different aspects of the critical behavior and that are nonperturbatively related. The second order of the derivative expansion fixes several issues that were encountered at the lower level and improves the compatibility with the droplet-theory predictions.

M. Bauer

The problem of time in the quantization of gravity arises from the fact that time in Schroedinger's equation is a parameter. This sets time apart from the spatial coordinates, represented by operators in quantum mechanics (QM). Thus "time" in QM and "time" in General Relativity (GR) are seen as mutually incompatible notions. The introduction of a dy- namical time operator in relativistic quantum mechanics (RQM), that in the Heisenberg representation is also a function of the parameter t (iden- tifed as the laboratory time), prompts to examine whether it can help to solve the disfunction referred to above. In particular, its application to the conditional interpretation of the canonical quantization approach toquantum gravity is developed. 1