Interference in the Wave Function of the Universe

As part of the quest to uncover universal features of quantum dynamics, we study catastrophes that form in simple many-body wave functions after a quench, focusing on two-mode systems that include the two-site Bose Hubbard model, and under some circumstances optomechanical systems and the Dicke model. When the wave function is plotted in Fock space plus time certain characteristic structures generically appear that we identify as cusp caustics. In the vicinity of such a catastrophe the wave function takes on a universal form described by the Pearcey function and obeys scaling relations which depend on the total number of particles $N$ . In the thermodynamic limit ( $N \rightarrow \infty$ ) the cusp becomes singular, but at finite $N$ it is decorated by an interference pattern. This pattern contains an intricate network of vortex-antivortex pairs, initiating a theory of topological structures in Fock space. In the case where the quench takes the form of a $\delta$ -kick we show how to analytically map the wave function onto the Pearcey function and hence obtain the scaling exponents for the size and position of the cusp, as well as those for the amplitude and characteristic length scales of its interference pattern.As part of the quest to uncover universal features of quantum dynamics, we study catastrophes that form in simple many-body wave functions after a quench, focusing on two-mode systems that include the two-site Bose Hubbard model, and under some circumstances optomechanical systems and the Dicke model. When the wave function is plotted in Fock space plus time certain characteristic structures generically appear that we identify as cusp caustics. In the vicinity of such a catastrophe the wave function takes on a universal form described by the Pearcey function and obeys scaling relations which depend on the total number of particles $N$. In the thermodynamic limit ($N \rightarrow \infty$) the cusp becomes singular, but at finite $N$ it is decorated by an interference pattern. This pattern contains an intricate network of vortex-antivortex pairs, initiating a theory of topological structures in Fock space. In the case where the quench takes the form of a $\delta$-kick we show how to analytically map the wave function onto the Pearcey function and hence obtain the scaling exponents for the size and position of the cusp, as well as those for the amplitude and characteristic length scales of its interference pattern.

Sep 15, 20160 citations

Interpreting the wave function of the universe

Frank J. Tipler

Physics ReportsMay 1, 198694 citations

Interference in Quantum Mechanics

Urbasi Sinha, Debadrita Ghosh

arXiv:2508.12940Journal of the Indian Institute of ScienceJan 1, 20252 citations

Interpreting the wave function

Jean-Luc Lehners

This chapter discusses how a classical universe arises out of the quantum wave function of the universe. The process of decoherence is described, first in general and then applied to cosmology. The classicalization of the background spacetime (and the associated reduction in interference between saddle points) as well as the classicalization of long-wavelength perturbation modes is discussed, by studying an example of interactions between background and fluctuations, as well as interaction between perturbation modes of different wavelengths. Comments on the interpretation of the wave function are included.This chapter discusses how a classical universe arises out of the quantum wave function of the universe. The process of decoherence is described, first in general and then applied to cosmology. The classicalization of the background spacetime (and the associated reduction in interference between saddle points) as well as the classicalization of long-wavelength perturbation modes is discussed, by studying an example of interactions between background and fluctuations, as well as interaction between perturbation modes of different wavelengths. Comments on the interpretation of the wave function are included.

Cambridge University Press eBooksFeb 2, 20260 citations

Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling

J. Mumford, W. Kirkby, Duncan H J O’Dell

Abstract As part of the quest to uncover universal features of quantum dynamics, we study catastrophes that form in simple many-particle wave functions following a quench, focusing on two-mode systems that include the two-site Bose–Hubbard model, and under some circumstances optomechanical systems and the Dicke model. When the wave function is plotted in Fock space certain characteristic shapes, that we identify as cusp catastrophes, appear under generic conditions. In the vicinity of a cusp the wave function takes on a universal structure described by the Pearcey function and obeys scaling relations which depend on the total number of particles N . In the thermodynamic limit ( N → ∞ ) the cusp becomes singular, but at finite N it is decorated by an interference pattern. This pattern contains an intricate network of vortex–antivortex pairs, initiating a theory of topological structures in Fock space. In the case where the quench is a δ -kick the problem can be solved analytically and we obtain scaling exponents for the size and position of the cusp, as well as those for the amplitude and characteristic length scales of its interference pattern. Finally, we use these scalings to describe the wave function in the critical regime of a Z 2 symmetry-breaking dynamical phase transition.Abstract As part of the quest to uncover universal features of quantum dynamics, we study catastrophes that form in simple many-particle wave functions following a quench, focusing on two-mode systems that include the two-site Bose–Hubbard model, and under some circumstances optomechanical systems and the Dicke model. When the wave function is plotted in Fock space certain characteristic shapes, that we identify as cusp catastrophes, appear under generic conditions. In the vicinity of a cusp the wave function takes on a universal structure described by the Pearcey function and obeys scaling relations which depend on the total number of particles N . In the thermodynamic limit ( N → ∞ ) the cusp becomes singular, but at finite N it is decorated by an interference pattern. This pattern contains an intricate network of vortex–antivortex pairs, initiating a theory of topological structures in Fock space. In the case where the quench is a δ -kick the problem can be solved analytically and we obtain scaling exponents for the size and position of the cusp, as well as those for the amplitude and characteristic length scales of its interference pattern. Finally, we use these scalings to describe the wave function in the critical regime of a Z 2 symmetry-breaking dynamical phase transition.

arXiv:1609.04502Journal of Physics B Atomic Molecular and Optical PhysicsJan 4, 201715 citations

The Wavefunction and the Wigner Function of the Universe

Hideo Kodama

数理解析研究所講究録Jun 1, 19920 citations

N

. In the thermodynamic limit (

N \rightarrow \infty

) the cusp becomes singular, but at finite

N

it is decorated by an interference pattern. This pattern contains an intricate network of vortex-antivortex pairs, initiating a theory of topological structures in Fock space. In the case where the quench takes the form of a

\delta

-kick we show how to analytically map the wave function onto the Pearcey function and hence obtain the scaling exponents for the size and position of the cusp, as well as those for the amplitude and characteristic length scales of its interference pattern.