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The statement announced in the title is proven., Comment: Comments welcome!

We demonstrate buffer gas cooling of carbon atoms to cryogenic temperatures. By employing pulsed two-photon excitation followed by vacuum ultraviolet fluorescence detection, we measured the arrival time distribution of the ablated carbon atoms to the detection volume at various helium buffer gas densities. The experimental data, corroborated by Monte Carlo simulations, reveal a rapid decrease in the local temperature of the carbon atom gas to approximately 10~K within tens of microseconds. The findings establish a major step towards novel research utilizing cold and ultracold carbon atoms., Comment: 10 pages, 3 figures

We prove the integral Varadhan short-time formula for non-linear heat flow on measured Finsler manifolds. To the best of the authors' knowledge, this is the first result establishing a Varadhan-type formula for non-linear semigroups. We do not assume the reversibility of the metric, and the distance function can be asymmetric. Within this generality, we reveal that the probabilistic interpretation is well-suited for our formula; the probability that a particle starting from a set $A$ can be found in another set $B$ describes the distance from $A$ to $B$. One side of the estimates (the upper bound of the probability) is also established in the nonsmooth setting of infinitesimally strictly convex metric measure spaces satisfying the local Sobolev-to-Lipschitz property., Comment: 24 pages, comments are welcomed!

We consider the Rademacher- and Sobolev-to-Lipschitz-type properties for arbitrary quasi-regular strongly local Dirichlet spaces. We discuss the persistence of these properties under localization, globalization, transfer to weighted spaces, tensorization, and direct integration. As byproducts we obtain: necessary and sufficient conditions to identify a quasi-regular strongly local Dirichlet form on an extended metric topological $\sigma$-finite possibly non-Radon measure space with the Cheeger energy of the space; the tensorization of intrinsic distances; the tensorization of the Varadhan short-time asymptotics., Comment: 40 pages, 2 figures

Let $\varUpsilon$ be the configuration space over a complete and separable metric base space, endowed with the Poisson measure $\pi$. We study the geometry of $\varUpsilon$ from the point of view of optimal transport and Ricci-lower bounds. To do so, we define a formal Riemannian structure on $\mathscr{P}_{1}(\varUpsilon)$, the space of probability measures over $\varUpsilon$ with finite first moment, and we construct an extended distance $\mathcal{W}$ on $\mathscr{P}_{1}(\varUpsilon)$. The distance $\mathcal{W}$ corresponds, in our setting, to the Benamou--Brenier variational formulation of the Wasserstein distance. Our main technical tool is a non-local continuity equation defined via the difference operator on the Poisson space. We show that the closure of the domain of the relative entropy is a complete geodesic space, when endowed with $\mathcal{W}$. We establish non-local infinite-dimensional analogues of results regarding the geometry of the Wasserstein space over a metric measure space with synthetic Ricci curvature bounded below. In particular, we obtain that: (a) the Ornstein--Uhlenbeck semi-group is the gradient flow of the relative entropy; (b) the Poisson space has a Ricci curvature, in the entropic sense, bounded below by $1$; (c) the distance $\mathcal{W}$ satisfies an HWI inequality., Comment: 45 pages, comments are welcome

We show that a differential structure associated with the infinite particle Dyson Brownian motion satisfies the Bakry-\'Emery nonnegative lower Ricci curvature bound $\mathsf{BE}(0, \infty)$. Various functional inequalities follow including a local spectral gap inequality, the Lipschitz Feller property, the dimension-free Harnack inequality and the evolutional variation inequality. As a consequence, the infinite Dyson Brownian motion is characterised as a gradient flow of the Boltzmann-Shannon entropy associated with $\mathsf{sine}_\beta$ point processes with respect to a certain Benamou-Brenier-like Wasserstein distance. At the end, we provide a sufficient condition for $\mathsf{BE}(K, \infty)$ beyond the Dyson model and apply it to the infinite particle model of the $\beta$-Riesz gas., Comment: 41 pages. Section 6 (Gradient Flow) has been added as an application of the main result. Corollary 1.2 has been shortened (local log-Sobolev inequality, local hyper-contractivity have been cut)

This paper proposes a new voice conversion (VC) task from human speech to dog-like speech while preserving linguistic information as an example of human to non-human creature voice conversion (H2NH-VC) tasks. Although most VC studies deal with human to human VC, H2NH-VC aims to convert human speech into non-human creature-like speech. Non-parallel VC allows us to develop H2NH-VC, because we cannot collect a parallel dataset that non-human creatures speak human language. In this study, we propose to use dogs as an example of a non-human creature target domain and define the "speak like a dog" task. To clarify the possibilities and characteristics of the "speak like a dog" task, we conducted a comparative experiment using existing representative non-parallel VC methods in acoustic features (Mel-cepstral coefficients and Mel-spectrograms), network architectures (five different kernel-size settings), and training criteria (variational autoencoder (VAE)- based and generative adversarial network-based). Finally, the converted voices were evaluated using mean opinion scores: dog-likeness, sound quality and intelligibility, and character error rate (CER). The experiment showed that the employment of the Mel-spectrogram improved the dog-likeness of the converted speech, while it is challenging to preserve linguistic information. Challenges and limitations of the current VC methods for H2NH-VC are highlighted., Comment: 5 pages, 4 figures

This is the second paper of a series on configuration spaces $\Upsilon$ over singular spaces $X$. Here, we focus on geometric aspects of the extended metric measure space $(\Upsilon, \mathsf{d}_{\Upsilon}, \mu)$ equipped with the $L^2$-transportation distance $\mathsf{d}_{\Upsilon}$, and a mixed Poisson measure $\mu$. Firstly, we establish the essential self-adjointness and the $L^p$-uniqueness for the Laplacian on $\Upsilon$ lifted from $X$. Secondly, we prove the equivalence of Bakry-\'Emery curvature bounds on $X$ and on $\Upsilon$, without any metric assumption on $X$. We further prove the Evolution Variation Inequality on $\Upsilon$, and introduce the notion of synthetic Ricci-curvature lower bounds for the extended metric measure space $\Upsilon$. As an application, we prove the Sobolev-to-Lipschitz property on $\Upsilon$ over singular spaces $X$, originally conjectured in the case when $X$ is a manifold by M. R\"ockner and A. Schield. As a further application, we prove the $L^\infty$-to-$\mathsf{d}_{\Upsilon}$-Lipschitz regularization of the heat semigroup on $\Upsilon$ and gives a new characterization of the ergodicity of the corresponding particle systems in terms of optimal transport., Comment: 50 pages

We study symmetric diffusion operators on metric measure spaces. Our main question is whether or not the restriction of the operator to a suitable core continues to be essentially self-adjoint or $L^p$-unique if a small closed set is removed from the space. The effect depends on how large the removed set is, and we provide characterizations of the critical size in terms of capacities and Hausdorff dimension. As a key tool we prove a truncation result for potentials of nonnegative functions. We apply our results to Laplace operators on Riemannian and sub-Riemannian manifolds and on metric measure spaces satisfying curvature dimension conditions. For non-collapsing Ricci limit spaces with two-sided Ricci curvature bounds we observe that the self-adjoint Laplacian is already fully determined by the classical Laplacian on the regular part.

In this paper, we provide relations among the following properties: (a) the tail triviality of a probability measure $\mu$ on the configuration space ${\boldsymbol\Upsilon}$; (b) the finiteness of the $L^2$-transportation-type distance $\bar{\mathsf d}_{{\boldsymbol\Upsilon}}$; (c) the irreducibility of $\mu$-symmetric Dirichlet forms on ${\boldsymbol\Upsilon}$. As an application, we obtain the ergodicity (i.e., the convergence to the equilibrium) of interacting infinite diffusions having logarithmic interaction arisen from determinantal/permanental point processes including $\mathrm{sine}_{2}$, $\mathrm{Airy}_{2}$, $\mathrm{Bessel}_{\alpha, 2}$ ($\alpha \ge 1$), and $\mathrm{Ginibre}$ point processes, in particular, the case of unlabelled Dyson Brownian motion is covered. For the proof, the number rigidity of point processes in the sense of Ghosh--Peres plays a key role., Comment: 35 pages, The choice of cores of Dirichlet forms is made flexible and not necessarily to be cylinder functions now. A new proof of the main result (Theorem I) does not rely on the Sobolev-to-Lipschitz property (SL), so that the description of (SL) is deleted. The base space is restricted to be the Euclidean space for the sake of simplicity. The transportation distance is modified to be a variant

We give a precise definition of BPS vortex loops in 3D non-abelian gauge theories with ${\cal N}=2$ SUSY by the path integral over fields with a prescribed singular behavior. We compute the expectation value of a BPS vortex loop on an ellipsoid. Using the result we revisit the known equivalence between Wilson and vortex loops in pure Chern-Simons theory. Naive computations of expectation values in ${\cal N}=2$ theory leads to an unwanted shift of parameters in the rule of correspondence. We resolve the problem by relating the shift to the global anomaly of ${\cal N}=2$ SUSY quantum mechanics. For theories with $U(N)$ gauge group we also develop an alternative description of vortex loops in terms of 1D ${\cal N}=2$ SUSY quantum mechanics on their worldline. For vortex loops in ${\cal N}=4$ theories, our construction reproduces some of the quiver GLSMs of Assel and Gomis., Comment: 58 pages; v2: a section added in the appendix, version to appear in JHEP

We prove the Sobolev-to-Lipschitz property for metric measure spaces satisfying the quasi curvature dimension condition recently introduced in E. Milman, The Quasi Curvature-Dimension Condition with applications to sub-Riemannian manifolds, Comm. Pure Appl. Math. (to appear, arXiv:1908.01513v5). We provide several applications to properties of the corresponding heat semigroup. In particular, under the additional assumption of infinitesimal Hilbertianity, we show the Varadhan short-time asymptotics for the heat semigroup with respect to the distance, and prove the irreducibility of the heat semigroup. These result apply in particular to large classes of (ideal) sub-Riemannian manifolds., Comment: 17 pages, to appear in Math. Ann

This paper contributes to foundations of the geometric measure theory in the infinite dimensional setting of the configuration space over the Euclidean space $\mathbb R^n$ equipped with the Poisson measure $\pi$. We first provide a rigorous meaning and construction of the $m$-codimensional Poisson measure -- formally written as "$(\infty-m)$-dimensional Poisson measure" -- on the configuration space. We then show that our construction is consistent with potential analysis by establishing the absolute continuity with respect to Bessel capacities. Secondly, we introduce three different definitions of BV functions based on the variational, relaxation and the semigroup approaches, and prove the equivalence of them. Thirdly, we construct perimeter measures and introduce the notion of the reduced boundary. We then prove that the perimeter measure can be expressed by the $1$-codimensional Poisson measure restricted on the reduced boundary, which is a generalisation of De Giorgi's identity to the configuration space. Finally, we construct the total variation measures for BV functions, and prove the Gau{\ss}--Green formula., Comment: 46 pages

We construct a canonical differential structure on the configuration space $\Upsilon$ over a singular base space $X$ and with a general invariant measure $\mu$ on $\Upsilon$. We present an analytic structure on $\Upsilon$, constructing a strongly local Dirichlet form $\mathcal E$ on $L^2(\Upsilon, \mu)$ for $\mu$ in a large class of probability measures. We then investigate the geometric structure of the extended metric measure space $\Upsilon$ endowed with the $L^2$-transportation extended distance $\mathsf{d}_{\Upsilon}$ and with the measure $\mu$. By establishing Rademacher- and Sobolev-to-Lipschitz-type properties for $\mathcal E$, we finally provide a complete identification of the analytic and the geometric structure -- the canonical differential structure induced on $\Upsilon$ by $X$ and $\mu$ -- showing that $\mathcal E$ coincides with the Cheeger energy of $(\Upsilon,\mathsf{d}_{\Upsilon},\mu)$ and that the intrinsic distance of $\mathcal E$ coincides with $\mathsf{d}_{\Upsilon}$. The class of base spaces to which our results apply includes sub-Riemannian manifolds, RCD spaces, and path/loop spaces over Riemannian manifolds; as for $\mu$ our results include quasi-Gibbs measures, in particular: Poisson measures, canonical Gibbs measures, as well as some determinantal/permanental point processes (sine$_\beta$, Airy$_\beta$, Bessel$_{\alpha,\beta}$, Ginibre). A number of applications to interacting particle systems and infinite-dimensional metric measure geometry are also discussed. In particular, we prove the universality of the $L^2$-transportation distance $\mathsf{d}_{\Upsilon}$ for the Varadhan short-time asymptotics for diffusions on $\Upsilon$, regardless of the choice of $\mu$. Many of our results are new even in the case of configuration spaces over Euclidean spaces., Comment: 85 pages, 3 diagrams, 3 tables (minor modifications, added table 3)

We extensively discuss the Rademacher and Sobolev-to-Lipschitz properties for generalized intrinsic distances on strongly local Dirichlet spaces possibly without square field operator. We present many non-smooth and infinite-dimensional examples. As an application, we prove the integral Varadhan short-time asymptotic with respect to a given distance function for a large class of strongly local Dirichlet forms., Comment: 44 pages, list of notations (end), Title, Abstract and Introduction have been changed. Lemma 2.10, Corollary 2.35, and Proposition 3.31 have been removed. Proposition 3.7 and Corollary 4.17 have been added

We analyze superconducting correlations in the one-dimensional Kondo lattice models with Ising anisotropy under transverse magnetic fields, using the density matrix renormalization group. For the spin-1/2 local spin model, the Ising anisotropy is introduced by the ferromagnetic Ising interaction between the local spins, while for the spin-1 model, it is taken by the single-ion anisotropy. The magnetic properties under the transverse fields for the spin-1/2 model are very similar to those for the spin-1 model [K. Suzuki and K. Hattori, J. Phys. Soc. Jpn. 88, 024707 (2019).]. For the superconducting correlations, we analyze various Cooper pairs within nearest-neighbor pairs including composite ones between the local spins and the electrons. We find that, for the spin-1/2 model, the superconducting correlations are highly enhanced in the Tomonaga-Luttinger liquid state near the Kondo-plateau phase, where the conduction electrons and the local spins are strongly coupled with a finite spin gap for the Ising axis. This is a clear contrast to the model under the longitudinal magnetic fields, where there are no noticeable superconducting correlations. Competitions between the transverse magnetic field and the Kondo singlet formation lead to this enhanced superconducting correlations. For the spin-1 model, the single-ion anisotropy suppresses the superconducting correlation and there is no noticeable enhancement. We also examine the large Kondo exchange coupling limit. For the moderate ferromagnetic Ising interaction between the local spins, we find that another type of superconducting correlation is enhanced inside the ferromagnetic phase. We discuss a possible relation between our results and reentrant superconductivity in U-based ferromagnetic superconductors under transverse magnetic fields., Comment: 17 pages, 12 figures

On the basis of the canonical quantization procedure, in which we need the indefinite metric Hilbert space, we formulate field diagonal representation for the scalar Lee-Wick model. Euclidean path integral for the model is then constructed in terms of the eigenvector of field operators. Taking the quantum mechanical Lee-Wick model as an example, we demonstrate how to formulate path integrals for such systems in detail. We show that, despite the use of indefinite metric representation, integration contours for ghost degrees can be taken along the real axis.

The Sobolev regularity of invariant measures for diffusion processes is proved on non-smooth metric measure spaces with synthetic lower Ricci curvature bounds. As an application, the symmetrizability of semigroups is characterized, and the stability of invariant measures is proved under perturbations of drifts and the underlying spaces in the sense of the measured Gromov convergence., Comment: 42 pages. Eq (5.1) and Condition (A') in p. 35 have been modified

We study the effects of transverse magnetic fields on the $S=1$ one-dimensional Kondo lattice model with a uniaxial anisotropy using the density matrix renormalization group. The model can be regarded as a simplified one for analyzing the Ising ferromagnetic superconductor URhGe. We find various phases such as ferromagnetic and antiferromagnetic phases, Kondo plateau (KP) phases, Tomonaga-Luttinger liquids, and fully polarized phases. In the KP phase, a pseudoplateau emerges in the magnetization due to strongly bound pairs between the local and the conduction electron spins. This is why we call this phase the Kondo plateau. At the critical field between the ferromagnetic and KP phases, we find metamagnetic behavior in the magnetization curve. We discuss various correlation functions and the Friedel oscillations in detail, and the experimental data under transverse magnetic fields in URhGe are discussed on the basis of the present results., Comment: 11 pages, 16 figures

We construct non-symmetric diffusion processes associated with Dirichlet forms consisting of uniformly elliptic forms and derivation operators with killing terms on RCD spaces by aid of non-smooth differential structures introduced by Gigli '16. After constructing diffusions, we investigate conservativeness and the weak convergence of the laws of diffusions in terms of a geometric convergence of the underling spaces and convergences of the corresponding coefficients., Comment: 41 pages. To appear in Calc. Var. PDEs. In the second version, the following have been modified: Section 2.3, 2.4, 2.5, 2.6 were added. Assumption 3.3, Proposition 3.4, Remark 3.5, and Example 3.7 were deleted. Example 7.2 was replaced with Corollary 7.2. Theorem 4.4 was modified

We show that the pointed measured Gromov convergence of the underlying spaces implies (or under some condition, is equivalent to) the weak convergence of Brownian motions under Riemannian Curvature-Dimension (RCD) conditions., Comment: 39 pages, 3 figures. Final version. To appear in EJP. Theorem 1.4 has been modified with the time interval [\epsilon, \infty]

Suppose that metric measure spaces X_n=(X_n, d_n, m_n) satisfy RCD(K,infty) conditions with m_n(X_n)=1. Then the measured Gromov convergence (introduced by Gigili-Mondino-Savare '13) of X_n is equivalent to the weak convergence of the laws of Brownian motions on X_n with initial distributions m_n., Comment: Withdrawn because the content of this paper has been fully included in my new manuscript arXiv:1703.07234

Suppose that a sequence of metric measure spaces X_n=(X_n, d_n, m_n) satisfies RCD*(K,N) with Diam(X_n)

Let $X$ be a compact metric space and $\mathcal M_X$ be the set of isometry classes of compact metric spaces $Y$ such that the Lipschitz distance $d_L(X,Y)$ is finite. We show that $(\mathcal M_X, d_L)$ is not separable when $X$ is a closed interval, or an infinite union of shrinking closed intervals., Comment: 17 pages, 2 figures