It is a fundamental assumption of statistical mechanics that a closed system with many degrees of freedom ergodically samples all equal energy points in phase space. To understand the limits of this assumption, it is important to find and study systems that are not ergodic, and thus do not reach thermal equilibrium. A few complex systems have been proposed that are expected not to thermalize because their dynamics are integrable. Some nearly integrable systems of many particles have been studied numerically, and shown not to ergodically sample phase space. However, there has been no experimental demonstration of such a system with many degrees of freedom that does not approach thermal equilibrium. Here we report the preparation of out-of-equilibrium arrays of trapped one-dimensional (1D) Bose gases, each containing from 40 to 250 (87)Rb atoms, which do not noticeably equilibrate even after thousands of collisions. Our results are probably explainable by the well-known fact that a homogeneous 1D Bose gas with point-like collisional interactions is integrable. Until now, however, the time evolution of out-of-equilibrium 1D Bose gases has been a theoretically unsettled issue, as practical factors such as harmonic trapping and imperfectly point-like interactions may compromise integrability. The absence of damping in 1D Bose gases may lead to potential applications in force sensing and atom interferometry.

We report the observation of a one-dimensional (1D) Tonks-Girardeau (TG) gas of bosons moving freely in 1D. Although TG gas bosons are strongly interacting, they behave very much like noninteracting fermions. We enter the TG regime with cold rubidium-87 atoms by trapping them with a combination of two light traps. By changing the trap intensities, and hence the atomic interaction strength, the atoms can be made to act either like a Bose-Einstein condensate or like a TG gas. We measure the total 1D energy and the length of the gas. With no free parameters and over a wide range of coupling strengths, our data fit the exact solution for the ground state of a 1D Bose gas.

We measure photoassociation rates in one-dimensional Bose gases, and so determine the local pair correlation function over a wide range of coupling strengths. As bosons become more strongly coupled, we observe a tenfold decrease in their wave function overlap, thus directly observing the fermionization of bosons.

BACKGROUNDThe authors sought to identify treatment‐related factors that influenced survival after surgical treatment for metastatic spinal tumors and to evaluate the relationship between survival and postoperative ambulation time as a factor related to quality of life.METHODSThe medical records of 81 patients with metastatic spinal tumors who underwent palliative surgery at the study institution were assessed. Univariate analysis for factors influencing survival used the Kaplan–Meier log rank statistic and multivariate analysis used the Cox proportional hazards model. The Spearman correlation test was used to analyze the relationship between postoperative ambulation and survival time.RESULTSThe patients had a median age of 59.9 years and a median survival of 10.6 months after surgery. For patients, postoperative ambulatory median survival was 16.5 months and median ambulation time was 13.8 months. By univariate analysis, anatomic site of the primary tumor, postoperative ambulation, and combined adjuvant therapy (chemotherapy plus radiotherapy) were associated with prolonged survival (P < 0.05). Multivariate analysis identified primary site and postoperative ambulatory function as independent predictors of prolonged survival (P < 0.0001). Significant correlations were found between ambulation time and survival time of patients who were able to walk after surgery (P < 0.0001), even in patients with liver (P < 0.05) or lung carcinoma (P < 0.05).CONCLUSIONSThe anatomic site of primary carcinoma and postoperative ambulation were associated with longer survival after palliative surgery for metastatic spinal tumor. When ambulation is attained after surgery, it can be preserved until late in remaining life even when the primary tumor is unfavorable. Palliative surgery for spinal metastasis can improve the quality and quantity of life. Cancer 2003;97:476–84. © 2003 American Cancer Society.DOI 10.1002/cncr.11039

Erythrocyte sedimentation rate and C-reactive protein display a significantly higher reaction after spinal surgery with instrumentation. Renewed elevation of C-reactive protein, white blood cell count, and body temperature after postoperative days 4 to 7 may be a critical sign of postoperative infection.