We study the quantum tunneling dynamics of many-body entangled solitons composed of ultracold bosonic gases in 1D optical lattices. A bright soliton, confined by a potential barrier, is allowed to tunnel out of confinement by reducing the barrier width and for varying strengths of attractive interactions. Simulation of the Bose Hubbard Hamiltonian is performed with time-evolving block decimation. We find the characteristic $1/e$ time for the escape of the soliton, substantially different from the mean field prediction, and address how many-body effects like quantum fluctuations, entanglement, and nonlocal correlations affect macroscopic quantum tunneling; number fluctuations and second order correlations are suggested as experimental signatures. We find that while the escape time scales exponentially in the interactions, the time at which both the von Neumann entanglement entropy and the slope of number fluctuations is maximized scale only linearly.We study the quantum tunneling dynamics of many-body entangled solitons composed of ultracold bosonic gases in 1D optical lattices. A bright soliton, confined by a potential barrier, is allowed to tunnel out of confinement by reducing the barrier width and for varying strengths of attractive interactions. Simulation of the Bose Hubbard Hamiltonian is performed with time-evolving block decimation. We find the characteristic $1/e$ time for the escape of the soliton, substantially different from the mean field prediction, and address how many-body effects like quantum fluctuations, entanglement, and nonlocal correlations affect macroscopic quantum tunneling; number fluctuations and second order correlations are suggested as experimental signatures. We find that while the escape time scales exponentially in the interactions, the time at which both the von Neumann entanglement entropy and the slope of number fluctuations is maximized scale only linearly.

arXiv:1105.5164May 25, 20118 citations

Structural Origin of Square-Root Mass Scaling inQuantum Tunnelling

Krishna Kingkar Pathak

Abstract Quantum tunnelling phenomena across physics and chemistry are governed by an exponential sensitivity to the effective mass associated with the tunnelling coordinate. Within semiclassical WKB and instanton formalisms, this dependence takes a characteristic form, $\ln \mathcal{R} \propto -\sqrt{M_{\mathrm{eff}}}$ , arising from the factorisation of the Euclidean action into mass-dependent and geometric contributions. Although this scaling is well established at the level of theory, its status as a unifying structural principle across distinct physical regimes has not been systematically clarified. In this work, we examine the extent to which the square-root effective-mass dependence functions as a universal semiclassical descriptor of tunnelling across radically different physical platforms. By reanalysing representative experimental datasets from molecular isotopologues, collective tunnelling in ultracold atomic systems, and macroscopic quantum escape in Josephson circuits, we demonstrate that the leading semiclassical trend persists over more than twenty orders of magnitude in tunnelling rate. When expressed in terms of $\ln \mathcal{R}$ versus $\sqrt{M_{\mathrm{eff}}}$ , all platforms exhibit near-linear behaviour, indicating that the dominant contribution to the tunnelling exponent is controlled by a common Euclidean-action structure rather than system-specific microscopic details. We further identify the physical mechanisms—finite temperature, dissipation, many-body effects, and mass-dependent barrier reshaping—that delimit the regime of validity of this leading-order scaling. Taken together, the results support the view that the $\sqrt{M_{\mathrm{eff}}}$ dependence reflects a form of mechanical similarity in imaginary time, providing an ontologically neutral and cross-domain organising principle for quantum tunnelling phenomena from molecular systems to engineered macroscopic quantum devices.Abstract Quantum tunnelling phenomena across physics and chemistry are governed by an exponential sensitivity to the effective mass associated with the tunnelling coordinate. Within semiclassical WKB and instanton formalisms, this dependence takes a characteristic form, $\ln \mathcal{R} \propto -\sqrt{M_{\mathrm{eff}}}$, arising from the factorisation of the Euclidean action into mass-dependent and geometric contributions. Although this scaling is well established at the level of theory, its status as a unifying structural principle across distinct physical regimes has not been systematically clarified. In this work, we examine the extent to which the square-root effective-mass dependence functions as a universal semiclassical descriptor of tunnelling across radically different physical platforms. By reanalysing representative experimental datasets from molecular isotopologues, collective tunnelling in ultracold atomic systems, and macroscopic quantum escape in Josephson circuits, we demonstrate that the leading semiclassical trend persists over more than twenty orders of magnitude in tunnelling rate. When expressed in terms of $\ln \mathcal{R}$ versus $\sqrt{M_{\mathrm{eff}}}$, all platforms exhibit near-linear behaviour, indicating that the dominant contribution to the tunnelling exponent is controlled by a common Euclidean-action structure rather than system-specific microscopic details. We further identify the physical mechanisms—finite temperature, dissipation, many-body effects, and mass-dependent barrier reshaping—that delimit the regime of validity of this leading-order scaling. Taken together, the results support the view that the $\sqrt{M_{\mathrm{eff}}}$ dependence reflects a form of mechanical similarity in imaginary time, providing an ontologically neutral and cross-domain organising principle for quantum tunnelling phenomena from molecular systems to engineered macroscopic quantum devices.

Feb 11, 20260 citations

1/e

time for the escape of the soliton, substantially different from the mean field prediction, and address how many-body effects like quantum fluctuations, entanglement, and nonlocal correlations affect macroscopic quantum tunneling; number fluctuations and second order correlations are suggested as experimental signatures. We find that while the escape time scales exponentially in the interactions, the time at which both the von Neumann entanglement entropy and the slope of number fluctuations is maximized scale only linearly.

\ln \mathcal{R} \propto -\sqrt{M_{\mathrm{eff}}}

, arising from the factorisation of the Euclidean action into mass-dependent and geometric contributions. Although this scaling is well established at the level of theory, its status as a unifying structural principle across distinct physical regimes has not been systematically clarified. In this work, we examine the extent to which the square-root effective-mass dependence functions as a universal semiclassical descriptor of tunnelling across radically different physical platforms. By reanalysing representative experimental datasets from molecular isotopologues, collective tunnelling in ultracold atomic systems, and macroscopic quantum escape in Josephson circuits, we demonstrate that the leading semiclassical trend persists over more than twenty orders of magnitude in tunnelling rate. When expressed in terms of

\ln \mathcal{R}

versus

\sqrt{M_{\mathrm{eff}}}

, all platforms exhibit near-linear behaviour, indicating that the dominant contribution to the tunnelling exponent is controlled by a common Euclidean-action structure rather than system-specific microscopic details. We further identify the physical mechanisms—finite temperature, dissipation, many-body effects, and mass-dependent barrier reshaping—that delimit the regime of validity of this leading-order scaling. Taken together, the results support the view that the

\sqrt{M_{\mathrm{eff}}}

dependence reflects a form of mechanical similarity in imaginary time, providing an ontologically neutral and cross-domain organising principle for quantum tunnelling phenomena from molecular systems to engineered macroscopic quantum devices.