Thermodynamic behavior of a one-dimensional Bose gas at low temperature

We show that the chemical potential of a one-dimensional (1D) interacting Bose gas exhibits a non-monotonic temperature dependence which is peculiar of superfluids. The effect is a direct consequence of the phononic nature of the excitation spectrum at large wavelengths exhibited by 1D Bose gases. For low temperatures $T$, we demonstrate that the coefficient in $T^2$ expansion of the chemical potential is entirely defined by the zero-temperature density dependence of the sound velocity. We calculate that coefficient along the crossover between the Bogoliubov weakly-interacting gas and the Tonks-Girardeau gas of impenetrable bosons. Analytic expansions are provided in the asymptotic regimes. The theoretical predictions along the crossover are confirmed by comparison with the exactly solvable Yang-Yang model in which the finite-temperature equation of state is obtained numerically by solving Bethe-{\it ansatz} equations. A 1D ring geometry is equivalent to imposing periodic boundary conditions and arising finite-size effects are studied in details. At $T=0$ we calculated various thermodynamic functions, including the inelastic structure factor, as a function of the number of atoms, pointing out the occurrence of important deviations from the thermodynamic limit.Comment: 14 pages, 16 figure

Beyond-Luttinger-liquid thermodynamics of a one-dimensional Bose gas with repulsive contact interactions

We present a thorough study of the thermodynamics of a one-dimensional repulsive Bose gas, focusing in particular on corrections beyond the Luttinger-liquid description. We compute the chemical potential, pressure, and contact as a function of temperature and gas parameter with an exact thermal Bethe ansatz. In addition, we provide interpretations of the main features in the analytically tractable regimes, based on a variety of approaches (Bogoliubov, hard core, Sommerfeld, and virial). The beyond-Luttinger-liquid thermodynamic effects are found to be nonmonotonic as a function of gas parameter. Such behavior is explained in terms of nonlinear dispersion and “negative excluded volume” effects, for weak and strong repulsion, respectively, responsible for the opposite sign corrections in the thermal next-to-leading term of the thermodynamic quantities at low temperatures. Our predictions can be applied to other systems including super Tonks-Girardeau gases, dipolar and Rydberg atoms, helium, quantum liquid droplets in bosonic mixtures, and impurities in a quantum bath.Peer ReviewedPostprint (published version

Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas

We reveal an intriguing anomaly in the temperature dependence of the specific heat of a one-dimensional Bose gas. The observed peak holds for arbitrary interaction and remembers a superfluid-to-normal phase transition in higher dimensions, but phase transitions are not allowed in one dimension. The presence of the anomaly signals a region of unpopulated states which behaves as an energy gap and is located below the hole branch in the excitation spectrum. The anomaly temperature is found to be of the same order of the energy of the maximum of the hole branch. We rely on the Bethe Ansatz to obtain the specific heat exactly and provide interpretations of the analytically tractable limits. The dynamic structure factor is computed with the Path Integral Monte Carlo method for the first time. We notice that at temperatures similar to the anomaly threshold, the energy of the thermal fluctuations become comparable with the maximal hole energy, leading to a qualitative change in the structure of excitations. This excitation pattern experiences the breakdown of the quasi-particle description for any value of the interaction strength at the anomaly, similarly to any superfluid phase transition at the critical temperature. We provide indications for future observations and how the hole anomaly can be employed for in-situ thermometry, identifying different collisional regimes and understanding other anomalies in atomic, solid-state, electronic, spin-chain and ladder systems.Peer ReviewedPostprint (published version

The Peroxymonocarbonate anion HCO4- as an effective oxidant in the gas phase: A mass spectrometric and theoretical study on the reaction with SO2

The peroxymonocarbonate anion, HCO4-, the covalent adduct between the carbon dioxideand hydrogen peroxide anion, effectively reacts with SO2 in the gas phase following three oxidative routes. Mass spectrometric and electronic structure calculations show that sulphur dioxide is oxidised through a common intermediate to the hydrogen sulphate anion, sulphur trioxide, and sulphur trioxide anion as primary products through formal HO2-, oxygen atom, and oxygen ion transfers. The hydrogen sulphite anion is also formed as a secondary product from the oxygen atom transfer path. The uncommon nucleophilic behaviour of HCO4- is disclosed by the Lewis acidic properties of SO2, an amphiphilic molecule that forms intermediates with characteristic and diagnostic geometries with peroxymonocarbonate

Static compliance and driving pressure are associated with ICU mortality in intubated COVID-19 ARDS

Background Pathophysiological features of coronavirus disease 2019-associated acute respiratory distress syndrome (COVID-19 ARDS) were indicated to be somewhat different from those described in nonCOVID-19 ARDS, because of relatively preserved compliance of the respiratory system despite marked hypoxemia. We aim ascertaining whether respiratory system static compliance (Crs), driving pressure (DP), and tidal volume normalized for ideal body weight (VT/kg IBW) at the 1st day of controlled mechanical ventilation are associated with intensive care unit (ICU) mortality in COVID-19 ARDS. Methods Observational multicenter cohort study. All consecutive COVID-19 adult patients admitted to 25 ICUs belonging to the COVID-19 VENETO ICU network (February 28th-April 28th, 2020), who received controlled mechanical ventilation, were screened. Only patients fulfilling ARDS criteria and with complete records of Crs, DP and VT/kg IBW within the 1st day of controlled mechanical ventilation were included. Crs, DP and VT/kg IBW were collected in sedated, paralyzed and supine patients. Results A total of 704 COVID-19 patients were screened and 241 enrolled. Seventy-one patients (29%) died in ICU. The logistic regression analysis showed that: (1) Crs was not linearly associated with ICU mortality (p value for nonlinearity = 0.01), with a greater risk of death for values < 48 ml/cmH(2)O; (2) the association between DP and ICU mortality was linear (p value for nonlinearity = 0.68), and increasing DP from 10 to 14 cmH(2)O caused significant higher odds of in-ICU death (OR 1.45, 95% CI 1.06-1.99); (3) VT/kg IBW was not associated with a significant increase of the risk of death (OR 0.92, 95% CI 0.55-1.52). Multivariable analysis confirmed these findings. Conclusions Crs < 48 ml/cmH(2)O was associated with ICU mortality, while DP was linearly associated with mortality. DP should be kept as low as possible, even in the case of relatively preserved Crs, irrespective of VT/kg IBW, to reduce the risk of death

Collective oscillations of a trapped atomic gas in low dimensions and thermodynamics of one-dimensional Bose gas

Ultracold atoms are exceptional tools to explore the physics of quantum matter. In fact, the high degree of tunability of ultracold Bose and Fermi gases makes them ideal systems for quantum simulation and for investigating macroscopic manifestations of quantum effects, such as superfluidity. In ultracold gas research, a central role is played by collective oscillations. They can be used to study different dynamical regimes, such as superfluid, collisional, or collisionless limits or to test the equation of state of the system. In this thesis, we present a unified description of collective oscillations in low dimensions covering both Bose and Fermi statistics, different trap geometries and zero as well as finite temperature, based on the formalism of hydrodynamics and sum rules. We discuss the different behaviour exhibited by the second excited breathing mode in the collisional regime at low temperature and in the collisionless limit at high temperature in a 1D trapped Bose gas with repulsive contact interaction. We show how this mode exhibits a single-valued excitation spectrum in the collisional regime and two different frequencies in the collisionless limit. Our predictions could be important for future research related to the thermalization and damping phenomena in this low-dimensional system. We show that 1D uniform Bose gases exhibit a non-monotonic temperature dependence of the chemical potential characterized by an increasing-with-temperature behaviour at low temperature. This is due to the thermal excitation of phonons and reveals an interesting analogy with the behaviour of superfluids. Finally, we investigate a gas with a finite number N of atoms in a ring geometry at T = 0. We discuss explicitly the deviations of the thermodynamic behaviour in the ring from the one in the large N limit